[10010010] |<article>Algorithm</article>
[10010020] |In [[mathematics]], [[computing]], [[linguistics]] and related disciplines, an '''algorithm''' is a sequence of instructions, often used for [[calculation]] and [[data processing]].
[10010030] |It is formally a type of [[effective method]] in which a list of well-defined instructions for completing a task will, when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end-state.
[10010040] |The transition from one state to the next is not necessarily [[deterministic]]; some algorithms, known as [[probabilistic algorithms]], incorporate randomness.
[10010050] |A partial formalization of the concept began with attempts to solve the [[Entscheidungsproblem]] (the "decision problem") posed by [[David Hilbert]] in 1928.
[10010060] |Subsequent formalizations were framed as attempts to define "[[effective calculability]]" (Kleene 1943:274) or "effective method" (Rosser 1939:225); those formalizations included the Gödel-Herbrand-Kleene [[Recursion (computer science)|recursive function]]s of 1930, 1934 and 1935, [[Alonzo Church]]'s [[lambda calculus]] of 1936, [[Emil Post]]'s "Formulation I" of 1936, and [[Alan Turing]]'s [[Turing machines]] of 1936-7 and 1939.
[10010070] |==Etymology== 
[10010080] |[[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwārizmī]], [[Persian people|Persian]] [[astronomer]] and [[mathematician]], wrote a [[treatise]] in [[Arabic]] in 825 AD, ''On Calculation with Hindu Numerals''.
[10010090] |(See [[algorism]]).
[10010100] |It was translated into [[Latin]] in the 12th century as ''Algoritmi de numero Indorum'' (al-Daffa 1977), which title was likely intended to mean "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's rendition of the author's name; but people misunderstanding the title treated ''Algoritmi'' as a Latin plural and this led to the word "algorithm" (Latin ''algorismus'') coming to mean "calculation method".
[10010110] |The intrusive "th" is most likely due to a [[false cognate]] with the [[Greek language|Greek]] (''arithmos'') meaning "number".
[10010120] |== Why algorithms are necessary: an informal definition == 
[10010130] |No generally accepted ''formal'' definition of "algorithm" exists yet.
[10010140] |An informal definition could be "an algorithm is a computer program that calculates something."
[10010150] |For some people, a program is only an algorithm if it stops eventually.
[10010160] |For others, a program is only an algorithm if it stops before a given number of calculation steps.
[10010170] |A prototypical example of an "algorithm" is Euclid's algorithm to determine the maximum common divisor of two integers greater than one: "subtract the smallest number from the biggest one, repeat until you get a zero or a one".
[10010180] |This procedure is know to stop always, and the number of subtractions needed is always smaller than the biggest of the two numbers.
[10010190] |We can derive clues to the issues involved and an informal meaning of the word from the following quotation from (boldface added):
[10010200] |<blockquote>  No human being can write fast enough, or long enough, or small enough to list all members of an enumerably infinite set by writing out their names, one after another, in some notation.
[10010210] |But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give '''explicit instructions for determining the nth member of the set''', for arbitrary finite n.
[10010220] |Such instructions are to be given quite explicitly, in a form in which '''they could be followed by a computing machine''', or by a '''human who is capable of carrying out only very elementary operations on symbols'''  </blockquote>
[10010230] |The words "enumerably infinite" mean "countable using integers perhaps extending to infinity".
[10010240] |Thus Boolos and Jeffrey are saying that an algorithm ''implies'' instructions for a process that "creates" output integers from an ''arbitrary'' "input" integer or integers that, in theory, can be chosen from 0 to infinity.
[10010250] |Thus we might expect an algorithm to be an algebraic equation such as '''y = m + n''' — two arbitrary "input variables" '''m''' and '''n''' that produce an output '''y'''.
[10010260] |As we see in [[Algorithm characterizations]] — the word algorithm implies much more than this, something on the order of (for our addition example): 
[10010270] |:Precise instructions (in language understood by "the computer") for a "fast, efficient, good" ''process'' that specifies the "moves" of "the computer" (machine or human, equipped with the necessary internally-contained information and capabilities) to find, decode, and then munch arbitrary input integers/symbols '''m''' and '''n''', symbols '''+''' and '''=''' ... and (reliably, correctly, "effectively") produce, in a "reasonable" [[time]], output-integer '''y''' at a specified place and in a specified format.
[10010280] |The concept of ''algorithm'' is also used to define the notion of [[decidability (logic)|decidability]].
[10010290] |That notion is central for explaining how [[formal system]]s come into being starting from a small set of [[axiom]]s and rules.
[10010300] |In [[logic]], the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.
[10010310] |From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of ''algorithm'' that suits both concrete (in some sense) and abstract usage of the term.
[10010320] |:''For a detailed presentation of the various points of view around the definition of "algorithm" see [[Algorithm characterizations]].
[10010330] |For examples of simple addition algorithms specified in the detailed manner described in [[Algorithm characterizations]], see [[Algorithm examples]].''
[10010340] |== Formalization of algorithms == 
[10010350] |Algorithms are essential to the way [[computer]]s process information, because a [[computer program]] is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards.
[10010360] |Thus, an algorithm can be considered to be any sequence of operations that can be performed by a [[Turing completeness|Turing-complete]] system.
[10010370] |Authors who assert this thesis include Savage (1987) and Gurevich (2000):
[10010380] |<blockquote>  ...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine (Gurevich 2000:1)...according to Savage [1987], an algorithm is a computational process defined by a Turing machine.
[10010390] |(Gurevich 2000:3)  </blockquote>
[10010400] |Typically, when an algorithm is associated with processing information, data are read from an input source or device, written to an output sink or device, and/or stored for further processing.
[10010410] |Stored data are regarded as part of the internal state of the entity performing the algorithm.
[10010420] |In practice, the state is stored in a [[data structure]], but an algorithm requires the internal data only for specific operation sets called [[abstract data type]]s.
[10010430] |For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise.
[10010440] |That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).
[10010450] |Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm.
[10010460] |Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by ''[[control flow|flow of control]]''.
[10010470] |So far, this discussion of the formalization of an algorithm has assumed the premises of [[imperative programming]].
[10010480] |This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means.
[10010490] |Unique to this conception of formalized algorithms is the [[assignment operation]], setting the value of a variable.
[10010500] |It derives from the intuition of "[[memory]]" as a scratchpad.
[10010510] |There is an example below of such an assignment.
[10010520] |For some alternate conceptions of what constitutes an algorithm see [[functional programming]] and [[logic programming]] .
[10010530] |=== Termination === 
[10010540] |Some writers restrict the definition of ''algorithm'' to procedures that eventually finish.
[10010550] |In such a category Kleene places the "''decision procedure'' or ''decision method'' or ''algorithm'' for the question" (Kleene 1952:136).
[10010560] |Others, including Kleene, include procedures that could run forever without stopping; such a procedure has been called a "computational method" (Knuth 1997:5) or "''calculation procedure'' or ''algorithm''" (Kleene 1952:137); however, Kleene notes that such a method must eventually exhibit "some object" (Kleene 1952:137).
[10010570] |Minsky makes the pertinent observation, in regards to determining whether an algorithm will eventually terminate (from a particular starting state): 
[10010580] |<blockquote>  But if the length of the process is not known in advance, then "trying" it may not be decisive, because if the process does go on forever — then at no time will we ever be sure of the answer (Minsky 1967:105).</blockquote>
[10010590] |As it happens, no other method can do any better, as was shown by [[Alan Turing]] with his celebrated result on the undecidability of the so-called [[halting problem]].
[10010600] |There is no algorithmic procedure for determining of arbitrary algorithms whether or not they terminate from given starting states.
[10010610] |The analysis of algorithms for their likelihood of termination is called [[termination analysis]].
[10010620] |See the examples of (im-)"proper" subtraction at [[partial function]] for more about what can happen when an algorithm fails for certain of its input numbers — e.g., (i) non-termination, (ii) production of "junk" (output in the wrong format to be considered a number) or no number(s) at all (halt ends the computation with no output), (iii) wrong number(s), or (iv) a combination of these.
[10010630] |Kleene proposed that the production of "junk" or failure to produce a number is solved by having the algorithm detect these instances and produce e.g., an error message (he suggested "0"), or preferably, force the algorithm into an endless loop (Kleene 1952:322).
[10010640] |Davis does this to his subtraction algorithm — he fixes his algorithm in a second example so that it is proper subtraction (Davis 1958:12-15).
[10010650] |Along with the logical outcomes "true" and "false" Kleene also proposes the use of a third logical symbol "u" — undecided (Kleene 1952:326) — thus an algorithm will always produce ''something'' when confronted with a "proposition".
[10010660] |The problem of wrong answers must be solved with an independent "proof" of the algorithm e.g., using induction: 
[10010670] |<blockquote>  We normally require auxiliary evidence for this (that the algorithm correctly defines a [[mu recursive function]]), e.g., in the form of an inductive proof that, for each argument value, the computation terminates with a unique value (Minsky 1967:186).</blockquote>
[10010680] |=== Expressing algorithms === 
[10010690] |Algorithms can be expressed in many kinds of notation, including [[natural language]]s, [[pseudocode]], [[flowchart]]s, and [[programming language]]s.
[10010700] |Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms.
[10010710] |Pseudocode and flowcharts are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements, while remaining independent of a particular implementation language.
[10010720] |Programming languages are primarily intended for expressing algorithms in a form that can be executed by a [[computer]], but are often used as a way to define or document algorithms.
[10010730] |There is a wide variety of representations possible and one can express a given [[Turing machine]] program as a sequence of machine tables (see more at [[finite state machine]] and [[state transition table]]), as flowcharts (see more at [[state diagram]]), or as a form of rudimentary [[machine code]] or [[assembly code]] called "sets of quadruples" (see more at [[Turing machine]]).
[10010740] |Sometimes it is helpful in the description of an algorithm to supplement small "flow charts" (state diagrams) with natural-language and/or arithmetic expressions written inside "[[block diagram]]s" to summarize what the "flow charts" are accomplishing.
[10010750] |Representations of algorithms are generally classed into three accepted levels of Turing machine description (Sipser 2006:157): 
[10010760] |*'''1 High-level description''':
[10010770] |:: "...prose to describe an algorithm, ignoring the implementation details.
[10010780] |At this level we do not need to mention how the machine manages its tape or head" 
[10010790] |*'''2 Implementation description''':
[10010800] |:: "...prose used to define the way the Turing machine uses its head and the way that it stores data on its tape.
[10010810] |At this level we do not give details of states or transition function" 
[10010820] |*'''3 Formal description''':
[10010830] |:: Most detailed, "lowest level", gives the Turing machine's "state table".
[10010840] |:''For an example of the simple algorithm "Add m+n" described in all three levels see [[Algorithm examples]].''
[10010850] |=== Implementation === 
[10010860] |Most algorithms are intended to be implemented as [[computer programs]].
[10010870] |However, algorithms are also implemented by other means, such as in a biological [[neural network]] (for example, the [[human brain]] implementing [[arithmetic]] or an insect looking for food), in an [[electrical circuit]], or in a mechanical device.
[10010880] |== Example == 
[10010890] |One of the simplest algorithms is to find the largest number in an (unsorted) list of numbers.
[10010900] |The solution necessarily requires looking at every number in the list, but only once at each.
[10010910] |From this follows a simple algorithm, which can be stated in a high-level description [[English language|English]] prose, as:
[10010920] |'''High-level description:''' 
[10010930] |# Assume the first item is largest.
[10010940] |# Look at each of the remaining items in the list and if it is larger than the largest item so far, make a note of it.
[10010950] |# The last noted item is the largest in the list when the process is complete.
[10010960] |'''(Quasi-)formal description:''' Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in [[pseudocode]] or [[pidgin code]]:
[10010970] |Input: A non-empty list of numbers ''L''.
[10010980] |Output: The ''largest'' number in the list ''L''. ''largest'' ← ''L''<sub>0</sub> '''for each''' ''item'' '''in''' the list ''L<sub>≥1</sub>'', '''do''' '''if''' the ''item'' > ''largest'', '''then''' ''largest'' ← the ''item'' '''return''' ''largest''
[10010990] |For a more complex example of an algorithm, see [[Euclid's algorithm]] for the [[greatest common divisor]], one of the earliest algorithms known.
[10011000] |=== Algorithm analysis === 
[10011010] |As it happens, it is important to know how much of a particular resource (such as time or storage) is required for a given algorithm.
[10011020] |Methods have been developed for the [[analysis of algorithms]] to obtain such quantitative answers; for example, the algorithm above has a time requirement of O(''n''), using the [[big O notation]] with ''n'' as the length of the list.
[10011030] |At all times the algorithm only needs to remember two values: the largest number found so far, and its current position in the input list.
[10011040] |Therefore it is said to have a space requirement of ''O(1)'', if the space required to store the input numbers is not counted, or O (log ''n'') if it is counted.
[10011050] |Different algorithms may complete the same task with a different set of instructions in less or more time, space, or effort than others.
[10011060] |For example, given two different recipes for making potato salad, one may have ''peel the potato'' before ''boil the potato'' while the other presents the steps in the reverse order, yet they both call for these steps to be repeated for all potatoes and end when the potato salad is ready to be eaten.
[10011070] |The [[analysis of algorithms|analysis and study of algorithms]] is a discipline of [[computer science]], and is often practiced abstractly without the use of a specific [[programming language]] or implementation.
[10011080] |In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation.
[10011090] |Usually [[pseudocode]] is used for analysis as it is the simplest and most general representation.
[10011100] |== Classes == 
[10011110] |There are various ways to classify algorithms, each with its own merits.
[10011120] |=== Classification by implementation === 
[10011130] |One way to classify algorithms is by implementation means.
[10011140] |* '''Recursion''' or '''iteration''': A [[recursive algorithm]] is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to [[functional programming]].
[10011150] |[[Iteration|Iterative]] algorithms use repetitive constructs like [[Control flow#Loops|loops]] and sometimes additional data structures like [[Stack (data structure)|stacks]] to solve the given problems.
[10011160] |Some problems are naturally suited for one implementation or the other.
[10011170] |For example, [[towers of hanoi]] is well understood in recursive implementation.
[10011180] |Every recursive version has an equivalent (but possibly more or less complex) iterative version, and vice versa.
[10011190] |* '''Logical''': An algorithm may be viewed as controlled [[Deductive reasoning|logical deduction]].
[10011200] |This notion may be expressed as: '''Algorithm = logic + control''' (Kowalski 1979).
[10011210] |The logic component expresses the axioms that may be used in the computation and the control component determines the way in which deduction is applied to the axioms.
[10011220] |This is the basis for the [[logic programming]] paradigm.
[10011230] |In pure logic programming languages the control component is fixed and algorithms are specified by supplying only the logic component.
[10011240] |The appeal of this approach is the elegant [[Formal semantics of programming languages|semantics]]: a change in the axioms has a well defined change in the algorithm.
[10011250] |* '''Serial''' or '''parallel''' or '''distributed''': Algorithms are usually discussed with the assumption that computers execute one instruction of an algorithm at a time.
[10011260] |Those computers are sometimes called serial computers.
[10011270] |An algorithm designed for such an environment is called a serial algorithm, as opposed to [[parallel algorithm]]s or [[distributed algorithms]].
[10011280] |Parallel algorithms take advantage of computer architectures where several processors can work on a problem at the same time, whereas distributed algorithms utilize multiple machines connected with a [[Computer Network|network]].
[10011290] |Parallel or distributed algorithms divide the problem into more symmetrical or asymmetrical subproblems and collect the results back together.
[10011300] |The resource consumption in such algorithms is not only processor cycles on each processor but also the communication overhead between the processors.
[10011310] |Sorting algorithms can be parallelized efficiently, but their communication overhead is expensive.
[10011320] |Iterative algorithms are generally parallelizable.
[10011330] |Some problems have no parallel algorithms, and are called inherently serial problems.
[10011340] |* '''Deterministic''' or '''non-deterministic''': [[Deterministic algorithm]]s solve the problem with exact decision at every step of the algorithm whereas [[non-deterministic algorithm]] solve problems via guessing although typical guesses are made more accurate through the use of [[heuristics]].
[10011350] |* '''Exact''' or '''approximate''': While many algorithms reach an exact solution, [[approximation algorithm]]s seek an approximation that is close to the true solution.
[10011360] |Approximation may use either a deterministic or a random strategy.
[10011370] |Such algorithms have practical value for many hard problems.
[10011380] |=== Classification by design paradigm === 
[10011390] |Another way of classifying algorithms is by their design methodology or paradigm.
[10011400] |There is a certain number of paradigms, each different from the other.
[10011410] |Furthermore, each of these categories will include many different types of algorithms.
[10011420] |Some commonly found paradigms include:
[10011430] |* '''Divide and conquer'''.
[10011440] |A [[divide and conquer algorithm]] repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually [[recursion|recursively]]), until the instances are small enough to solve easily.
[10011450] |One such example of divide and conquer is [[mergesort|merge sorting]].
[10011460] |Sorting can be done on each segment of data after dividing data into segments and sorting of entire data can be obtained in conquer phase by merging them.
[10011470] |A simpler variant of divide and conquer is called '''decrease and conquer algorithm''', that solves an identical subproblem and uses the solution of this subproblem to solve the bigger problem.
[10011480] |Divide and conquer divides the problem into multiple subproblems and so conquer stage will be more complex than decrease and conquer algorithms.
[10011490] |An example of decrease and conquer algorithm is [[binary search algorithm]].
[10011500] |* '''[[Dynamic programming]]'''.
[10011510] |When a problem shows [[optimal substructure]], meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems, and [[overlapping subproblems]], meaning the same subproblems are used to solve many different problem instances, a quicker approach called ''dynamic programming'' avoids recomputing solutions that have already been computed.
[10011520] |For example, the shortest path to a goal from a vertex in a weighted [[graph (mathematics)|graph]] can be found by using the shortest path to the goal from all adjacent vertices.
[10011530] |Dynamic programming and [[memoization]] go together.
[10011540] |The main difference between dynamic programming and divide and conquer is that subproblems are more or less independent in divide and conquer, whereas subproblems overlap in dynamic programming.
[10011550] |The difference between dynamic programming and straightforward recursion is in caching or memoization of recursive calls.
[10011560] |When subproblems are independent and there is no repetition, memoization does not help; hence dynamic programming is not a solution for all complex problems.
[10011570] |By using memoization or maintaining a [[Mathematical table|table]] of subproblems already solved, dynamic programming reduces the exponential nature of many problems to polynomial complexity.
[10011580] |* '''The greedy method'''.
[10011590] |A [[greedy algorithm]] is similar to a [[dynamic programming|dynamic programming algorithm]], but the difference is that solutions to the subproblems do not have to be known at each stage; instead a "greedy" choice can be made of what looks best for the moment.
[10011600] |The greedy method extends the solution with the best possible decision (not all feasible decisions) at an algorithmic stage based on the current local optimum and the best decision (not all possible decisions) made in previous stage.
[10011610] |It is not exhaustive, and does not give accurate answer to many problems.
[10011620] |But when it works, it will be the fastest method.
[10011630] |The most popular greedy algorithm is finding the minimal spanning tree as given by [[kruskal's algorithm|Kruskal]].
[10011640] |* '''Linear programming'''.
[10011650] |When solving a problem using [[linear programming]], specific [[inequality|inequalities]] involving the inputs are found and then an attempt is made to maximize (or minimize) some linear function of the inputs.
[10011660] |Many problems (such as the [[Maximum flow problem|maximum flow]] for directed [[graph (mathematics)|graphs]]) can be stated in a linear programming way, and then be solved by a 'generic' algorithm such as the [[simplex algorithm]].
[10011670] |A more complex variant of linear programming is called integer programming, where the solution space is restricted to the [[integers]].
[10011680] |* '''[[Reduction (complexity)|Reduction]]'''.
[10011690] |This technique involves solving a difficult problem by transforming it into a better known problem for which we have (hopefully) [[asymptotically optimal]] algorithms.
[10011700] |The goal is to find a reducing algorithm whose [[Computational complexity theory|complexity]] is not dominated by the resulting reduced algorithm's.
[10011710] |For example, one [[selection algorithm]] for finding the median in an unsorted list involves first sorting the list (the expensive portion) and then pulling out the middle element in the sorted list (the cheap portion).
[10011720] |This technique is also known as ''transform and conquer''.
[10011730] |* '''Search and enumeration'''.
[10011740] |Many problems (such as playing [[chess]]) can be modeled as problems on [[graph theory|graphs]].
[10011750] |A [[graph exploration algorithm]] specifies rules for moving around a graph and is useful for such problems.
[10011760] |This category also includes [[search algorithm]]s, [[branch and bound]] enumeration and [[backtracking]].
[10011770] |* '''The probabilistic and heuristic paradigm'''.
[10011780] |Algorithms belonging to this class fit the definition of an algorithm more loosely.
[10011790] |# [[Probabilistic algorithm]]s are those that make some choices randomly (or pseudo-randomly); for some problems, it can in fact be proven that the fastest solutions must involve some [[randomness]].
[10011800] |# [[Genetic algorithm]]s attempt to find solutions to problems by mimicking biological [[evolution]]ary processes, with a cycle of random mutations yielding successive generations of "solutions".
[10011810] |Thus, they emulate reproduction and "survival of the fittest".
[10011820] |In [[genetic programming]], this approach is extended to algorithms, by regarding the algorithm itself as a "solution" to a problem.
[10011830] |# [[Heuristic]] algorithms, whose general purpose is not to find an optimal solution, but an approximate solution where the time or resources are limited.
[10011840] |They are not practical to find perfect solutions.
[10011850] |An example of this would be [[local search (optimization)|local search]], [[tabu search]], or [[simulated annealing]] algorithms, a class of heuristic probabilistic algorithms that vary the solution of a problem by a random amount.
[10011860] |The name "[[simulated annealing]]" alludes to the metallurgic term meaning the heating and cooling of metal to achieve freedom from defects.
[10011870] |The purpose of the random variance is to find close to globally optimal solutions rather than simply locally optimal ones, the idea being that the random element will be decreased as the algorithm settles down to a solution.
[10011880] |=== Classification by field of study === 
[10011890] |Every field of science has its own problems and needs efficient algorithms.
[10011900] |Related problems in one field are often studied together.
[10011910] |Some example classes are [[search algorithm]]s, [[sorting algorithm]]s, [[merge algorithm]]s, [[numerical analysis|numerical algorithms]], [[graph theory|graph algorithms]], [[string algorithms]], [[computational geometry|computational geometric algorithms]], [[combinatorial|combinatorial algorithms]], [[machine learning]], [[cryptography]], [[data compression]] algorithms and [[parsing|parsing techniques]].
[10011920] |Fields tend to overlap with each other, and algorithm advances in one field may improve those of other, sometimes completely unrelated, fields.
[10011930] |For example, dynamic programming was originally invented for optimization of resource consumption in industry, but is now used in solving a broad range of problems in many fields.
[10011940] |=== Classification by complexity === 
[10011950] |Algorithms can be classified by the amount of time they need to complete compared to their input size.
[10011960] |There is a wide variety: some algorithms complete in linear time relative to input size, some do so in an exponential amount of time or even worse, and some never halt.
[10011970] |Additionally, some problems may have multiple algorithms of differing complexity, while other problems might have no algorithms or no known efficient algorithms.
[10011980] |There are also mappings from some problems to other problems.
[10011990] |Owing to this, it was found to be more suitable to classify the problems themselves instead of the algorithms into equivalence classes based on the complexity of the best possible algorithms for them.
[10012000] |=== Classification by computing power === 
[10012010] |Another way to classify algorithms is by computing power.
[10012020] |This is typically done by considering some collection (class) of algorithms.
[10012030] |A recursive class of algorithms is one that includes algorithms for all Turing computable functions.
[10012040] |Looking at classes of algorithms allows for the possibility of restricting the available computational resources (time and memory) used in a computation.
[10012050] |A subrecursive class of algorithms is one in which not all Turing computable functions can be obtained.
[10012060] |For example, the algorithms that run in [[P (complexity)|polynomial time]] suffice for many important types of computation but do not exhaust all Turing computable functions.
[10012070] |The class algorithms implemented by [[primitive recursive function]]s is another subrecursive class.
[10012080] |Burgin (2005, p. 24) uses a generalized definition of algorithms that relaxes the common requirement that the output of the algorithm that computes a function must be determined after a finite number of steps.
[10012090] |He defines a super-recursive class of algorithms as "a class of algorithms in which it is possible to compute functions not computable by any Turing machine" (Burgin 2005, p. 107).
[10012100] |This is closely related to the study of methods of [[hypercomputation]].
[10012110] |== Legal issues == 
[10012120] |:''See also: [[Software patents]] for a general overview of the patentability of software, including computer-implemented algorithms.''
[10012130] |Algorithms, by themselves, are not usually patentable.
[10012140] |In the [[United States]], a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals do not constitute "processes" (USPTO 2006) and hence algorithms are not patentable (as in [[Gottschalk v. Benson]]).
[10012150] |However, practical applications of algorithms are sometimes patentable.
[10012160] |For example, in [[Diamond v. Diehr]], the application of a simple [[feedback]] algorithm to aid in the curing of [[synthetic rubber]] was deemed patentable.
[10012170] |The [[Software patent debate|patenting of software]] is highly controversial, and there are highly criticized patents involving algorithms, especially [[data compression]] algorithms, such as [[Unisys]]' [[Graphics Interchange Format#Unisys and LZW patent enforcement|LZW patent]].
[10012180] |Additionally, some cryptographic algorithms have export restrictions (see [[export of cryptography]]).
[10012190] |== History: Development of the notion of "algorithm" == 
[10012200] |=== Origin of the word === 
[10012210] |The word ''algorithm'' comes from the name of the 9th century [[Persian people|Persian]] mathematician [[al-Khwarizmi|Abu Abdullah Muhammad ibn Musa al-Khwarizmi]] whose works introduced Indian numerals and algebraic concepts.
[10012220] |He worked in [[Baghdad]] at the time when it was the centre of scientific studies and trade.
[10012230] |The word ''[[algorism]]'' originally referred only to the rules of performing [[arithmetic]] using [[Hindu-Arabic numeral system|Arabic numerals]] but evolved via European Latin translation of al-Khwarizmi's name into ''algorithm'' by the 18th century.
[10012240] |The word evolved to include all definite procedures for solving problems or performing tasks.
[10012250] |=== Discrete and distinguishable symbols === 
[10012260] |'''Tally-marks''': To keep track of their flocks, their sacks of grain and their money the ancients used tallying: accumulating stones or marks scratched on sticks, or making discrete symbols in clay.
[10012270] |Through the Babylonian and Egyptian use of marks and symbols, eventually [[Roman numerals]] and the [[abacus]] evolved (Dilson, p.16–41).
[10012280] |Tally marks appear prominently in [[unary numeral system]] arithmetic used in [[Turing machine]] and [[Post-Turing machine]] computations.
[10012290] |=== Manipulation of symbols as "place holders" for numbers: algebra === 
[10012300] |The work of the Ancient Greek geometers, Persian mathematician [[Al-Khwarizmi]] (often considered as the "father of [[algebra]]"), and Western European mathematicians culminated in [[Leibniz]]'s notion of the [[calculus ratiocinator]] (ca 1680): 
[10012310] |:"A good century and a half ahead of his time, Leibniz proposed an algebra of logic, an algebra that would specify the rules for manipulating logical concepts in the manner that ordinary algebra specifies the rules for manipulating numbers" (Davis 2000:1)
[10012320] |=== Mechanical contrivances with discrete states === 
[10012330] |'''The clock''': Bolter credits the invention of the weight-driven [[clock]] as “The key invention [of Europe in the Middle Ages]", in particular the [[verge escapement]]< (Bolter 1984:24) that provides us with the tick and tock of a mechanical clock.
[10012340] |“The accurate automatic machine” (Bolter 1984:26) led immediately to "mechanical [[automata]]" beginning in the thirteenth century and finally to “computational machines" – the [[difference engine]] and [[analytical engine]]s of [[Charles Babbage]] and Countess [[Ada Lovelace]] (Bolter p.33–34, p.204–206).
[10012350] |'''Jacquard loom, Hollerith punch cards, telegraphy and telephony — the electromechanical relay''': Bell and Newell (1971) indicate that the [[Jacquard loom]] (1801), precursor to [[Hollerith cards]] (punch cards, 1887), and “telephone switching technologies” were the roots of a tree leading to the development of the first computers (Bell and Newell diagram p. 39, cf Davis 2000).
[10012360] |By the mid-1800s the [[telegraph]], the precursor of the telephone, was in use throughout the world, its discrete and distinguishable encoding of letters as “dots and dashes” a common sound.
[10012370] |By the late 1800s the [[ticker tape]] (ca 1870s) was in use, as was the use of [[Hollerith cards]] in the 1890 U.S. census.
[10012380] |Then came the [[Teletype]] (ca 1910) with its punched-paper use of [[Baudot code]] on tape.
[10012390] |Telephone-switching networks of electromechanical [[relay]]s (invented 1835) was behind the work of [[George Stibitz]] (1937), the inventor of the digital adding device.
[10012400] |As he worked in Bell Laboratories, he observed the “burdensome’ use of mechanical calculators with gears.
[10012410] |"He went home one evening in 1937 intending to test his idea....
[10012420] |When the tinkering was over, Stibitz had constructed a binary adding device".
[10012430] |(Valley News, p. 13).
[10012440] |Davis (2000) observes the particular importance of the electromechanical relay (with its two "binary states" ''open'' and ''closed''): 
[10012450] |: It was only with the development, beginning in the 1930s, of electromechanical calculators using electrical relays, that machines were built having the scope Babbage had envisioned."
[10012460] |(Davis, p. 14).
[10012470] |=== Mathematics during the 1800s up to the mid-1900s === 
[10012480] |'''Symbols and rules''': In rapid succession the mathematics of [[George Boole]] (1847, 1854), [[Gottlob Frege]] (1879), and [[Giuseppe Peano]] (1888–1889) reduced arithmetic to a sequence of symbols manipulated by rules.
[10012490] |Peano's ''The principles of arithmetic, presented by a new method'' (1888) was "the first attempt at an axiomatization of mathematics in a symbolic language" (van Heijenoort:81ff).
[10012500] |But Heijenoort gives Frege (1879) this kudos: Frege’s is "perhaps the most important single work ever written in logic. ... in which we see a " 'formula language', that is a ''lingua characterica'', a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments ... constructed from specific symbols that are manipulated according to definite rules" (van Heijenoort:1).
[10012510] |The work of Frege was further simplified and amplified by [[Alfred North Whitehead]] and [[Bertrand Russell]] in their [[Principia Mathematica]] (1910–1913).
[10012520] |'''The paradoxes''': At the same time a number of disturbing paradoxes appeared in the literature, in particular the [[Burali-Forti paradox]] (1897), the [[Russell paradox]] (1902–03), and the [[Richard Paradox]] (Dixon 1906, cf Kleene 1952:36–40).
[10012530] |The resultant considerations led to [[Kurt Gödel]]’s paper (1931) — he specifically cites the paradox of the liar — that completely reduces rules of [[recursion]] to numbers.
[10012540] |'''Effective calculability''': In an effort to solve the [[Entscheidungsproblem]] defined precisely by Hilbert in 1928, mathematicians first set about to define what was meant by an "effective method" or "effective calculation" or "effective calculability" (i.e., a calculation that would succeed).
[10012550] |In rapid succession the following appeared: [[Alonzo Church]], [[Stephen Kleene]] and [[J.B. Rosser]]'s [[λ-calculus]], (cf footnote in [[Alonzo Church]] 1936a:90, 1936b:110) a finely-honed definition of "general recursion" from the work of Gödel acting on suggestions of [[Jacques Herbrand]] (cf Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene (1935-6:237ff, 1943:255ff). Church's proof (1936:88ff) that the [[Entscheidungsproblem]] was unsolvable, [[Emil Post]]'s definition of effective calculability as a worker mindlessly following a list of instructions to move left or right through a sequence of rooms and while there either mark or erase a paper or observe the paper and make a yes-no decision about the next instruction (cf "Formulation I", Post 1936:289-290).
[10012560] |[[Alan Turing]]'s proof of that the Entscheidungsproblem was unsolvable by use of his "a- [automatic-] machine"(Turing 1936-7:116ff) -- in effect almost identical to Post's "formulation", [[J. Barkley Rosser]]'s definition of "effective method" in terms of "a machine" (Rosser 1939:226).
[10012570] |[[S. C. Kleene]]'s proposal of a precursor to "[[Church thesis]]" that he called "Thesis I" (Kleene 1943:273–274), and a few years later Kleene's renaming his Thesis "Church's Thesis" (Kleene 1952:300, 317) and proposing "Turing's Thesis" (Kleene 1952:376).
[10012580] |=== Emil Post (1936) and Alan Turing (1936-7, 1939)=== 
[10012590] |Here is a remarkable coincidence of two men not knowing each other but describing a process of men-as-computers working on computations — and they yield virtually identical definitions.
[10012600] |[[Emil Post]] (1936) described the actions of a "computer" (human being) as follows: 
[10012610] |:"...two concepts are involved: that of a ''symbol space'' in which the work leading from problem to answer is to be carried out, and a fixed unalterable ''set of directions''.
[10012620] |His symbol space would be 
[10012630] |:"a two way infinite sequence of spaces or boxes...
[10012640] |The problem solver or worker is to move and work in this symbol space, being capable of being in, and operating in but one box at a time.... a box is to admit of but two possible conditions, i.e., being empty or unmarked, and having a single mark in it, say a vertical stroke.
[10012650] |:"One box is to be singled out and called the starting point. ...a specific problem is to be given in symbolic form by a finite number of boxes [i.e., INPUT] being marked with a stroke.
[10012660] |Likewise the answer [i.e., OUTPUT] is to be given in symbolic form by such a configuration of marked boxes....
[10012670] |:"A set of directions applicable to a general problem sets up a deterministic process when applied to each specific problem.
[10012680] |This process will terminate only when it comes to the direction of type (C ) [i.e., STOP]." (U p. 289–290) See more at [[Post-Turing machine]]
[10012690] |[[Alan Turing]]’s work (1936, 1939:160) preceded that of Stibitz (1937); it is unknown whether Stibitz knew of the work of Turing.
[10012700] |Turing’s biographer believed that Turing’s use of a typewriter-like model derived from a youthful interest: “Alan had dreamt of inventing typewriters as a boy; Mrs. Turing had a typewriter; and he could well have begun by asking himself what was meant by calling a typewriter 'mechanical'" (Hodges, p. 96).
[10012710] |Given the prevalence of Morse code and telegraphy, ticker tape machines, and Teletypes we might conjecture that all were influences.
[10012720] |Turing — his model of computation is now called a [[Turing machine]] — begins, as did Post, with an analysis of a human computer that he whittles down to a simple set of basic motions and "states of mind".
[10012730] |But he continues a step further and creates a machine as a model of computation of numbers (Turing 1936-7:116).
[10012740] |:"Computing is normally done by writing certain symbols on paper.
[10012750] |We may suppose this paper is divided into squares like a child's arithmetic book....I assume then that the computation is carried out on one-dimensional paper, i.e., on a tape divided into squares.
[10012760] |I shall also suppose that the number of symbols which may be printed is finite....
[10012770] |:"The behavior of the computer at any moment is determined by the symbols which he is observing, and his "state of mind" at that moment.
[10012780] |We may suppose that there is a bound B to the number of symbols or squares which the computer can observe at one moment.
[10012790] |If he wishes to observe more, he must use successive observations.
[10012800] |We will also suppose that the number of states of mind which need be taken into account is finite...
[10012810] |:"Let us imagine that the operations performed by the computer to be split up into 'simple operations' which are so elementary that it is not easy to imagine them further divided" (Turing 1936-7:136).
[10012820] |Turing's reduction yields the following:
[10012830] |:"The simple operations must therefore include:
[10012840] |::"(a) Changes of the symbol on one of the observed squares
[10012850] |::"(b) Changes of one of the squares observed to another square within L squares of one of the previously observed squares.
[10012860] |"It may be that some of these change necessarily invoke a change of state of mind.
[10012870] |The most general single operation must therefore be taken to be one of the following: 
[10012880] |::"(A) A possible change (a) of symbol together with a possible change of state of mind.
[10012890] |::"(B) A possible change (b) of observed squares, together with a possible change of state of mind"
[10012900] |:"We may now construct a machine to do the work of this computer."
[10012910] |(Turing 1936-7:136)
[10012920] |A few years later, Turing expanded his analysis (thesis, definition) with this forceful expression of it: 
[10012930] |:"A function is said to be "effectively calculable" if its values can be found by some purely mechanical process.
[10012940] |Although it is fairly easy to get an intuitive grasp of this idea, it is neverthessless desirable to have some more definite, mathematical expressible definition . . . [he discusses the history of the definition pretty much as presented above with respect to Gödel, Herbrand, Kleene, Church, Turing and Post] . . .
[10012950] |We may take this statement literally, understanding by a purely mechanical process one which could be carried out by a machine.
[10012960] |It is possible to give a mathematical description, in a certain normal form, of the structures of these machines.
[10012970] |The development of these ideas leads to the author's definition of a computable function, and to an identification of computability † with effective calculability . . . .
[10012980] |::"† We shall use the expression "computable function" to mean a function calculable by a machine, and we let "effectively calculabile" refer to the intuitive idea without particular identification with any one of these definitions."(Turing 1939:160)
[10012990] |=== J. B. Rosser (1939) and S. C. Kleene (1943) === 
[10013000] |'''[[J. Barkley Rosser]]''' boldly defined an ‘effective [mathematical] method’ in the following manner (boldface added): 
[10013010] |:"'Effective method' is used here in the rather special sense of a method each step of which is precisely determined and which is certain to produce the answer in a finite number of steps.
[10013020] |With this special meaning, three different precise definitions have been given to date. [his footnote #5; see discussion immediately below].
[10013030] |The simplest of these to state (due to Post and Turing) says essentially that '''an effective method of solving certain sets of problems exists if one can build a machine which will then solve any problem of the set with no human intervention beyond inserting the question and (later) reading the answer'''.
[10013040] |All three definitions are equivalent, so it doesn't matter which one is used.
[10013050] |Moreover, the fact that all three are equivalent is a very strong argument for the correctness of any one."
[10013060] |(Rosser 1939:225–6)
[10013070] |Rosser's footnote #5 references the work of (1) Church and Kleene and their definition of λ-definability, in particular Church's use of it in his ''An Unsolvable Problem of Elementary Number Theory'' (1936); (2) Herbrand and Gödel and their use of recursion in particular Gödel's use in his famous paper ''On Formally Undecidable Propositions of Principia Mathematica and Related Systems I'' (1931); and (3) Post (1936) and Turing (1936-7) in their mechanism-models of computation.
[10013080] |'''[[Stephen C. Kleene]]''' defined as his now-famous "Thesis I" known as the [[Church-Turing thesis]].
[10013090] |But he did this in the following context (boldface in original): 
[10013100] |:"12.
[10013110] |'''Algorithmic theories'''...
[10013120] |In setting up a complete algorithmic theory, what we do is to describe a procedure, performable for each set of values of the independent variables, which procedure necessarily terminates and in such manner that from the outcome we can read a definite answer, "yes" or "no," to the question, "is the predicate value true?”"
[10013130] |(Kleene 1943:273)
[10013140] |=== History after 1950 === 
[10013150] |A number of efforts have been directed toward further refinement of the definition of "algorithm", and activity is on-going because of issues surrounding, in particular, [[foundations of mathematics]] (especially the [[Church-Turing Thesis]]) and [[philosophy of mind]] (especially arguments around [[artificial intelligence]]).
[10013160] |For more, see [[Algorithm characterizations]].
[10013170] |==Algorithmic Repositories== 
[10013180] |*LEDA
[10013190] |*Stanford GraphBase
[10013200] |*Combinatorica
[10013210] |*Netlib
[10013220] |*XTango
[10020010] |<article>Ambiguity</article>
[10020020] |'''Ambiguity''' is the property of being '''ambiguous''', where a [[word]], term, notation, sign, [[symbol]], [[phrase]], [[Sentence (linguistics)|sentence]], or any other form used for [[communication]], is called ambiguous if it can be interpreted in more than one way.
[10020030] |Ambiguity is distinct from ''[[vagueness]]'', which arises when the boundaries of meaning are indistinct.
[10020040] |Ambiguity is context-dependent: the same communication may be ambiguous in one context and unambiguous in another context.
[10020050] |For a word, ambiguity typically refers to an unclear choice between different definitions as may be found in a [[dictionary]].
[10020060] |A sentence may be ambiguous due to different ways of [[parsing]] the same sequence of words.
[10020070] |== Linguistic forms == 
[10020080] |'''[[Polysemy|Lexical ambiguity]]''' arises when [[context]] is insufficient to determine the sense of a single word that has more than one meaning.
[10020090] |For example, the word “bank” has several distinct definitions, including “financial institution” and “edge of a river,” but if someone says “I deposited $100 in the bank,” most people would not think you used a shovel to dig in the mud.
[10020100] |The word "run" has 130 ambiguous definitions in some [[lexicon]]s.
[10020110] |"Biweekly" can mean "fortnightly" (once every two weeks - 26 times a year), OR "twice a week" (104 times a year).
[10020120] |Stating a specific context like "meeting schedule" does NOT disambiguate "biweekly."
[10020130] |Many people believe that such lexically-ambiguous, miscommunication-prone words should be avoided altogether, since the user generally has to waste time, effort, and [[attention span]] to define what is meant when they are used.
[10020140] |The use of multi-defined words requires the author or speaker to clarify their context, and sometimes elaborate on their specific intended meaning (in which case, a less ambiguous term should have been used).
[10020150] |The goal of clear concise communication is that the receiver(s) have no misunderstanding about what was meant to be conveyed.
[10020160] |An exception to this could include a politician whose "wiggle words" and [[obfuscation]] are necessary to gain support from multiple [[constituent (politics)]] with [[mutually exclusive]] conflicting desires from their candidate of choice.
[10020170] |Ambiguity is a powerful tool of [[political science]].
[10020180] |More problematic are words whose senses express closely-related concepts.
[10020190] |“Good,” for example, can mean “useful” or “functional” (''That’s a good hammer''), “exemplary” (''She’s a good student''), “pleasing” (''This is good soup''), “moral” (''a good person'' versus ''the lesson to be learned from a story''), "[[righteous]]", etc.
[10020200] |“I have a good daughter” is not clear about which sense is intended.
[10020210] |The various ways to apply [[prefix]]es and [[suffix]]es can also create ambiguity (“unlockable” can mean “capable of being unlocked” or “impossible to lock”, and therefore should not be used).
[10020220] |'''[[Syntactic ambiguity]]''' arises when a sentence can be [[parsing|parsed]] in more than one way.
[10020230] |“He ate the cookies on the couch,” for example, could mean that he ate those cookies which were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies.
[10020240] |[[Spoken language]] can contain many more types of ambiguities, where there is more than one way to compose a set of sounds into words, for example “ice cream” and “I scream.”
[10020250] |Such ambiguity is generally resolved based on the context.
[10020260] |A mishearing of such, based on incorrectly-resolved ambiguity, is called a [[mondegreen]].
[10020270] |'''[[Meaning (non-linguistic)|Semantic ambiguity]]''' arises when a word or concept has an inherently diffuse meaning based on widespread or informal usage.
[10020280] |This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion.
[10020290] |For example, “You could do with a new automobile.
[10020300] |How about a test drive?”
[10020310] |The clause “You could do with” presents a statement with such wide possible interpretation as to be essentially meaningless.
[10020320] |Lexical ambiguity is contrasted with semantic ambiguity.
[10020330] |The former represents a choice between a finite number of known and meaningful context-dependent interpretations.
[10020340] |The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning.
[10020350] |This form of ambiguity is closely related to [[vagueness]].
[10020360] |Linguistic ambiguity can be a problem in law (see [[Ambiguity (law)]]), because the interpretation of written documents and oral agreements is often of paramount importance.
[10020370] |==Intentional application== 
[10020380] |[[Philosopher]]s (and other users of [[logic]]) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments, because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments.
[10020390] |For example, a politician might say “I oppose taxes that hinder economic growth.”
[10020400] |Some will think he opposes taxes in general, because they hinder economic growth.
[10020410] |Others may think he opposes only those taxes that he believes will hinder economic growth (although in writing, the correct insertion or omission of a [[comma (punctuation)|comma]] after “taxes” and the use of "which" can help reduce ambiguity here.
[10020420] |For the first meaning, “, which” is properly used in place of “that”), or restructure the sentence to completely eliminate possible misinterpretation.
[10020430] |The devious politician hopes that each [[constituent (politics)]] will interpret the above statement in the most desirable way, and think the politician supports everyone's opinion.
[10020440] |However, the opposite can also be true - An opponent can turn a positive statement into a bad one, if the speaker uses ambiguity (intentionally or not).
[10020450] |The logical fallacies of [[amphiboly]] and [[equivocation]] rely heavily on the use of ambiguous words and phrases.
[10020460] |In [[literature]] and [[rhetoric]], on the other hand, ambiguity can be a useful tool.
[10020470] |[[Groucho Marx]]’s classic joke depends on a grammatical ambiguity for its [[humor]], for example: “Last night I shot an elephant in my pajamas.
[10020480] |What he was doing in my pajamas I’ll never know.”
[10020490] |Ambiguity can also be used as a comic device through a genuine intention to confuse, as does Magic: The Gathering's Unhinged © Ambiguity, which makes puns with [[homophone]]s, mispunctuation, and run-ons: “Whenever a player plays a spell that counters a spell that has been played[,] or a player plays a spell that comes into play with counters, that player may counter the next spell played[,] or put an additional counter on a permanent that has already been played, but not countered.”
[10020500] |Songs and poetry often rely on ambiguous words for artistic effect, as in the song title “Don’t It Make My Brown Eyes Blue” (where “blue” can refer to the color, or to [[sadness]]).
[10020510] |In narrative, ambiguity can be introduced in several ways: motive, plot, character.
[10020520] |[[F. Scott Fitzgerald]] uses the latter type of ambiguity with notable effect in his novel ''[[The Great Gatsby]]''.
[10020530] |All [[religions]] debate the [[orthodoxy]] or [[heterodoxy]] of ambiguity.
[10020540] |[[Christianity]] and [[Judaism]] employ the concept of [[paradox]] synonymously with 'ambiguity'.
[10020550] |Ambiguity within Christianity (and other religions) is resisted by the conservatives and fundamentalists, who regard the concept as equating with 'contradiction'.
[10020560] |Non-fundamentalist Christians and Jews endorse [[Rudolf Otto]]'s description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans.
[10020570] |[[Metonymy]] involves the use of the name of a subcomponent part as an abbreviation, or [[jargon]], for the name of the whole object (for example "wheels" to refer to a car, or "flowers" to refer to beautiful offspring, an entire plant, or a collection of blooming plants).
[10020580] |In modern [[vocabulary]] critical [[semiotics]], metonymy encompasses any potentially-ambiguous word substitution that is based on contextual [[contiguity]] (located close together), or a function or process that an object performs, such as "sweet ride" to refer to a nice car.
[10020590] |Metonym miscommunication is considered a primary mechanism of linguistic humour.
[10020600] |==Psychology and management== 
[10020610] |In sociology and social psychology, the term "ambiguity" is used to indicate situations that involve [[uncertainty]].
[10020620] |An increasing amount of research is concentrating on how people react and respond to ambiguous situations.
[10020630] |Much of this focuses on [[ambiguity tolerance]].
[10020640] |A number of correlations have been found between an individual’s reaction and tolerance to ambiguity and a range of factors.
[10020650] |Apter and Desselles (2001) for example, found a strong correlation with such attributes and factors like a greater preference for safe as opposed to risk based sports, a preference for endurance type activities as opposed to explosive activities, a more organized and less casual lifestyle, greater care and precision in descriptions, a lower sensitivity to emotional and unpleasant words, a less acute sense of humour, engaging a smaller variety of sexual practices than their more risk comfortable colleagues, a lower likelihood of the use of drugs, pornography and drink, a greater likelihood of displaying obsessional behaviour.
[10020660] |In the field of [[leadership]] [[David Wilkinson (ambiguity expert)|David Wilkinson]] (2006) found strong correlations between an individual leaders reaction to ambiguous situations and the [[Modes of Leadership]] they use, the type of [[creativity]] (Kirton (2003) and how they relate to others.
[10020670] |==Music== 
[10020680] |In [[music]], pieces or sections which confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some [[polytonality]], [[polymeter]], other ambiguous [[metre|meters]] or [[rhythm]]s, and ambiguous [[phrase (music)|phrasing]], or (Stein 2005, p.79) any [[aspect of music]].
[10020690] |The [[music of Africa]] is often purposely ambiguous.
[10020700] |To quote [[Donald Francis Tovey|Sir Donald Francis Tovey]] (1935, p.195), “Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value.”
[10020710] |==Constructed language== 
[10020720] |Some [[Conlang|languages have been created]] with the intention of avoiding ambiguity, especially lexical ambiguity.
[10020730] |[[Lojban]] and [[Loglan]] are two related languages which have been created with this in mind.
[10020740] |The languages can be both spoken and written.
[10020750] |These languages are intended to provide a greater technical precision over natural languages, although historically, such attempts at language improvement have been criticized.
[10020760] |Languages composed from many diverse sources contain much ambiguity and inconsistency.
[10020770] |The many exceptions to [[syntax]] and [[semantic]] rules are time-consuming and difficult to learn.
[10020780] |==Mathematics and physics== 
[10020790] |[[Mathematical notation]], widely used in [[physics]] and other [[science]]s, avoids many ambiguities compared to expression in natural language.
[10020800] |However, for various reasons, several [[Lexical (semiotics)|lexical]], [[syntactic]] and [[semantic]] ambiguities remain.
[10020810] |===Names of functions=== 
[10020820] |The <b>ambiguity<b> in the style of writing a function should not be confused with a [[multivalued function]], which can (and should) be defined in a deterministic and unambiguous way.
[10020830] |Several [[special function]]s still do not have established notations.
[10020840] |Usually, the conversion to another notation requires to scale the argument and/or the resulting value; sometimes, the same name of the function is used, causing confusions.
[10020850] |Examples of such underestablished functions: 
[10020860] |* [[Sinc function]] 
[10020870] |* [[Elliptic integral#Complete_elliptic_integral_of_the_third_kind|Elliptic integral of the Third Kind]]; translating elliptic integral form [[MAPLE]] to [[Mathematica]], one should replace the second argument to its square, see [[Talk:Elliptic integral#List_of_notations]]; dealing with complex values, this may cause problems.
[10020880] |* [[Exponential integral]], , page 228 http://www.math.sfu.ca/~cbm/aands/page_228.htm
[10020890] |* [[Hermite polynomial]], , page 775 http://www.math.sfu.ca/~cbm/aands/page_775.htm
[10020900] |===Expressions=== 
[10020910] |Ambiguous espressions often appear in physical and mathematical texts.
[10020920] |It is common practice to omit multiplication signs in mathematical expressions.
[10020930] |Also, it is common, to give the same name to a variable and a function, for example, <math>~f=f(x)~</math>.
[10020940] |Then, if one sees <math>~g=f(y+1)~</math>, there is no way to distinguish, does it mean <math>~f=f(x)~</math> '''multiplied''' by <math>~(y+1)~</math>, or function <math>~f~</math> '''evaluated''' at argument equal to <math>~(y+1)~</math>.
[10020950] |In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.
[10020960] |Creators of algorithmic languages try to avoid ambiguities.
[10020970] |Many algorithmic languages ([[C++]], [[MATLAB]], [[Fortran]], [[Maple]]) require the character * as symbol of multiplication.
[10020980] |The language [[Mathematica]] allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions.
[10020990] |Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression '''f=f(x)''' is qualified as an error.
[10021000] |The order of operations may depend on the context.
[10021010] |In most [[programming language]]s, the operations of division and multiplication have equal priority and are executed from left to right.
[10021020] |Until the last century, many editorials assumed that multiplication is performed first, for example, <math>~a/bc~</math> is interpreted as <math>~a/(bc)~</math>; in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language.
[10021030] |In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity.
[10021040] |Sometimes, one uses ''italics'' letters to denote elementary functions.
[10021050] |In the [[scientific journal]] style, the expression <math>~ s i n \alpha~</math> means product of variables <math>~s~</math>, <math>~i~</math>, <math>~n~</math> and <math>~\alpha~</math>, although in a slideshow, it may mean <math>~\sin[\alpha]~</math>.
[10021060] |Comma in subscripts and superscripts sometimes is omitted; it is also ambiguous notation.
[10021070] |If it is written <math>~T_{mnk}~</math>, the reader should guess from the context, does it mean a single-index object, evaluated while the subscript is equal to product of variables <math>~m~</math>, <math>~n~</math> and <math>~k~</math>, or it is indication to a three-valent tensor.
[10021080] |The writing of <math>~T_{mnk}~</math> instead of <math>~T_{m,n,k}~</math> may mean that the writer either is stretched in space (for example, to reduce the publication fees, or aims to increase number of publications without considering readers.
[10021090] |The same may apply to any other use of ambiguous notations.
[10021100] |===Examples of potentially confusing ambiguous mathematical expressions === 
[10021110] |<math>\sin^2\alpha/2\,</math>, which could be understood to mean either <math>(\sin(\alpha/2))^2\,</math> or <math>(\sin(\alpha))^2/2\,</math>.
[10021120] |<math>~\sin^{-1} \alpha</math>, which by convention means <math>~\arcsin(\alpha) ~</math>, though it might be thought to mean <math>(\sin(\alpha))^{-1}\,</math> since <math>~\sin^{n} \alpha</math> means <math>(\sin(\alpha))^{n}\,</math>.
[10021130] |<math>a/2b\,</math>, which arguably should mean <math>(a/2)b\,</math> but would commonly be understood to mean <math>a/(2b)\,</math>
[10021140] |===Notations in [[quantum optics]] and [[quantum mechanics]]=== 
[10021150] |It is common to define the [[coherent states]] in [[quantum optics]] with <math>~|\alpha\rangle~ </math> and states with fixed number of photons with <math>~|n\rangle~</math>.
[10021160] |Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and <math>~n~</math>photon state if the Latin characters dominate.
[10021170] |The ambiguity becomes even worse, if <math>~|x\rangle~</math> is used for the states with certain value of the coordinate, and <math>~|p\rangle~</math> means the state with certain value of the momentum, which may be used in books on [[quantum mechanics]].
[10021180] |Such ambiguities easy lead to confusions, especially if some normalized [[adimensional]], [[dimensionless]] variables are used.
[10021190] |Expression <math> |1\rangle </math> may mean a state with single photon, or the coherent state with mean amplitude equal to 1, or state with momentum equal to unity, and so on.
[10021200] |The reader is supposed to guess from the context.
[10021210] |===Examples of ambiguous terms in physics=== 
[10021220] |Some physical quantities do not yet have established notations; their value (and sometimes even [[dimension]], as in the case of the [[Einstein coefficients]]) depends on the system of notations.
[10021230] |A highly confusing term is [[gain]].
[10021240] |For example, the sentence "the gain of a system should be doubled", without context, means close to nothing.
[10021250] |It may mean that the ratio of the output voltage of an electric circuit to the input voltage should be doubled.
[10021260] |It may mean that the ratio of the output power of an electric or optical circuit to the input power should be doubled.
[10021270] |It may mean that the gain of the laser medium should be doubled, for example, doubling the population of the upper laser level in a quasi-two level system (assuming negligible absorption of the ground-state).
[10021280] |Also, confusions may be related with the use of [[atomic percent]] as measure of concentration of a [[dopant]], or [[Optical resolution|resolution]] of an [[imaging system]], as measure of the size of the smallest detail which still can be resolved at the background of statistical noise.
[10021290] |See also [[Accuracy and precision]] and its talk.
[10021300] |Many terms are ambiguous.
[10021310] |Each use of an ambiguous term should be preceded by the definition, suitable for a specific case.
[10021320] |The [[Berry paradox]] arises as a result of systematic ambiguity.
[10021330] |In various formulations of the Berry paradox, such as one that reads: ''The number not nameable in less than eleven syllables'' the term ''nameable'' is one that has this systematic ambiguity.
[10021340] |Terms of this kind give rise to [[vicious circle]] fallacies.
[10021350] |Other terms with this type of ambiguity are: satisfiable, definable, true, false, function, property, class, relation, cardinal, and ordinal.
[10021360] |==Pedagogic use of ambiguous expressions== 
[10021370] |Ambiguity can be used as a pedagogical trick, to force students to reproduce the deduction by themselves.
[10021380] |Some textbooks give the same name to the function and to its [[Fourier transform]]: 
[10021390] |:<math>~f(\omega)=\int f(t) \exp(i\omega t) {\rm d}t </math>.
[10021400] |Rigorously speaking, such an expression requires that <math>~ f=0 ~</math>; even if function <math>~ f ~</math> is a [[self-Fourier function]], the expression should be written as <math>~f(\omega)=\frac{1}{\sqrt{2\pi}}\int f(t) \exp(i\omega t) {\rm d}t </math>; however, <b>it is assumed that the shape of the function </b> (and even its norm <math>\int |f(x)|^2 {\rm d}x </math>) <b>depend on the character used to denote its argument<b>.
[10021410] |If the Greek letter is used, it is assumed to be a [[Fourier transform]] of another function, The first function is assumed, if the expression in the argument contains more characters <math>~t~</math> or <math>~\tau~</math>, than characters <math>~\omega~</math>, and the second function is assumed in the opposite case.
[10021420] |Expressions like <math>~f(\omega t)~</math> or <math>~f(y)~</math> contain symbols <math>~t~</math> and <math>~\omega~</math> in equal amounts; they are ambiguous and should be avoided in serious deduction.
[10030010] |<article>Artificial intelligence</article>
[10030020] |'''Artificial intelligence (AI)''' is both the [[intelligence]] of machines and the branch of [[computer science]] which aims to create it.
[10030030] |Major AI textbooks define artificial intelligence as "the study and design of [[intelligent agents]]," where an [[intelligent agent]] is a system that perceives its environment and takes actions which maximize its chances of success.
[10030040] |[[John McCarthy (computer scientist)|John McCarthy]], who coined the term in 1956, defines it as "the science and engineering of making intelligent machines."
[10030050] |Among the traits that researchers hope machines will exhibit are [[:#Deduction, reasoning, problem solving|reasoning]], [[#Knowledge representation|knowledge]], [[#Planning|planning]], [[#Learning|learning]], [[#Natural language processing|communication]], [[#Perception|perception]] and the ability to [[#Motion and manipulation|move]] and manipulate objects.
[10030055] |[[#General intelligence|General intelligence]] (or "[[strong AI]]") has not yet been achieved and is a long-term goal of some AI research.
[10030060] |AI research uses tools and insights from many fields, including [[computer science]], [[psychology]], [[philosophy]], [[neuroscience]], [[cognitive science]], [[computational linguistics|linguistics]], [[ontology (information science)|ontology]], [[operations research]], [[computational economics|economics]], [[control theory]], [[probability]], [[optimization (mathematics)|optimization]] and [[logic]].
[10030070] |AI research also overlaps with tasks such as [[robotics]], [[control system]]s, [[automated planning and scheduling|scheduling]], [[data mining]], [[logistics]], [[speech recognition]], [[facial recognition system|facial recognition]] and many others.
[10030080] |Other names for the field have been proposed, such as [[computational intelligence]], [[synthetic intelligence]], [[intelligent systems]], or computational rationality.
[10030090] |== Perspectives on AI == 
[10030100] |=== AI in myth, fiction and speculation === 
[10030110] |Humanity has imagined in great detail the implications of thinking machines or artificial beings.
[10030120] |They appear in [[Greek myth]]s, such as [[Talos]] of [[Crete]], the golden robots of [[Hephaestus]] and [[Pygmalion (mythology)|Pygmalion's]] [[Galatea (mythology)|Galatea]].
[10030130] |The earliest known humanoid robots (or [[automaton]]s) were [[cult image|sacred statue]]s worshipped in [[Egypt]] and [[Greece]], believed to have been endowed with genuine consciousness by craftsman.
[10030140] |In the sixteenth century, the [[alchemist]] [[Paracelsus]] claimed to have created artificial beings.
[10030150] |Realistic clockwork imitations of human beings have been built by people such as [[King Mu of Zhou#Robotics|Yan Shi]], [[Hero of Alexandria]], [[Al-Jazari]] and [[Wolfgang von Kempelen]].
[10030160] |In modern fiction, beginning with [[Mary Shelley]]'s classic ''[[Frankenstein]],'' writers have explored the [[ethics of artificial intelligence|ethical]] issues presented by thinking machines.
[10030170] |If a machine can be created that has intelligence, can it also ''feel''?
[10030180] |If it can feel, does it have the same rights as a human being?
[10030190] |This is a key issue in ''[[Frankenstein]]'' as well as in modern science fiction: for example, the film ''[[Artificial Intelligence: A.I.]]'' considers a machine in the form of a small boy which has been given the ability to feel human emotions, including, tragically, the capacity to suffer.
[10030200] |This issue is also being considered by [[futurist]]s, such as California's [[Institute for the Future]] under the name "[[robot rights]]", although many critics believe that the discussion is premature.
[10030210] |[[Science fiction]] writers and [[futurist]]s have also speculated on the technology's potential impact on humanity.
[10030220] |In fiction, AI has appeared as a servant ([[R2D2]] in ''[[Star Wars]]''), a comrade ([[Data (Star Trek)|Lt. Commander Data]] in ''[[Star Trek]]''), an extension to human abilities (''[[Ghost in the Shell]]''), a conqueror (''[[The Matrix]]''), a dictator (''[[With Folded Hands]]'') and an exterminator (''[[Terminator (series)|Terminator]]'', ''[[Battlestar Galactica (re-imagining)|Battlestar Galactica]]'').
[10030230] |Some realistic potential consequences of AI are decreased human labor demand, the enhancement of human ability or experience, and a need for redefinition of human identity and basic values.
[10030240] |[[Futurist]]s estimate the capabilities of machines using [[Moore's Law]], which measures the relentless exponential improvement in digital technology with uncanny accuracy.
[10030250] |[[Ray Kurzweil]] has calculated that [[desktop computer]]s will have the same processing power as human brains by the year 2029, and that by 2045 artificial intelligence will reach a point where it is able to improve ''itself'' at a rate that far exceeds anything conceivable in the past, a scenario that [[science fiction]] writer [[Vernor Vinge]] named the "[[technological singularity]]".
[10030260] |"Artificial intelligence is the next stage in evolution," [[Edward Fredkin]] said in the 1980s, expressing an idea first proposed by [[Samuel Butler (novelist)|Samuel Butler]]'s ''[[Darwin Among the Machines]]'' (1863), and expanded upon by [[George Dyson (science historian)|George Dyson]] in his book of the same name (1998).
[10030270] |Several [[futurist]]s and [[science fiction]] writers have predicted that human beings and machines will merge in the future into [[cyborg]]s that are more capable and powerful than either.
[10030280] |This idea, called [[transhumanism]], has roots in [[Aldous Huxley]] and [[Robert Ettinger]], is now associated with [[robotics|robot]] designer [[Hans Moravec]], [[cybernetics|cyberneticist]] [[Kevin Warwick]] and [[Ray Kurzweil]].
[10030290] |[[Transhumanism]] has been illustrated in fiction as well, for example on the [[manga]] ''[[Ghost in the Shell]]''
[10030300] |=== History of AI research === 
[10030310] |In the middle of the 20th century, a handful of scientists began a new approach to building intelligent machines, based on recent discoveries in [[neurology]], a new mathematical theory of [[information]], an understanding of control and stability called [[cybernetic]]s, and above all, by the invention of the [[digital computer]], a machine based on the abstract essence of mathematical reasoning.
[10030320] |The field of modern AI research was founded at conference on the campus of [[Dartmouth College]] in the summer of 1956.
[10030330] |Those who attended would become the leaders of AI research for many decades, especially [[John McCarthy (computer scientist)|John McCarthy]], [[Marvin Minsky]], [[Allen Newell]] and [[Herbert Simon]], who founded AI laboratories at [[MIT]], [[Carnegie Mellon University|CMU]] and [[Stanford]].
[10030340] |They and their students wrote programs that were, to most people, simply astonishing: computers were solving word problems in algebra, proving logical theorems and speaking English.
[10030350] |By the middle 60s their research was heavily funded by the [[DARPA|U.S. Department of Defense]] and they were optimistic about the future of the new field: 
[10030360] |* 1965, [[H. A. Simon]]: "[M]achines will be capable, within twenty years, of doing any work a man can do"
[10030370] |* 1967, [[Marvin Minsky]]: "Within a generation ... the problem of creating 'artificial intelligence' will substantially be solved."
[10030380] |These predictions, and many like them, would not come true.
[10030390] |They had failed to recognize the difficulty of some of the problems they faced.
[10030400] |In 1974, in response to the criticism of England's [[Sir James Lighthill]] and ongoing pressure from Congress to fund more productive projects, the U.S. and British governments cut off all undirected, exploratory research in AI.
[10030410] |This was the first [[AI Winter]].
[10030420] |In the early 80s, AI research was revived by the commercial success of [[expert systems]] (a form of AI program that simulated the knowledge and analytical skills of one or more human experts) and by 1985 the market for AI had reached more than a billion dollars.
[10030430] |[[Marvin Minsky|Minsky]] and others warned the community that enthusiasm for AI had spiraled out of control and that disappointment was sure to follow.
[10030440] |Beginning with the collapse of the [[Lisp Machine]] market in 1987, AI once again fell into disrepute, and a second, more lasting [[AI Winter]] began.
[10030450] |In the 90s and early 21st century AI achieved its greatest successes, albeit somewhat behind the scenes.
[10030460] |Artificial intelligence was adopted throughout the technology industry, providing the heavy lifting for [[logistics]], [[data mining]], [[medical diagnosis]] and many other areas.
[10030470] |The success was due to several factors: the incredible power of computers today (see [[Moore's law]]), a greater emphasis on solving specific subproblems, the creation of new ties between AI and other fields working on similar problems, and above all a new commitment by researchers to solid mathematical methods and rigorous scientific standards.
[10030480] |=== Philosophy of AI === 
[10030490] |In a [[Computing Machinery and Intelligence|classic 1950 paper]], [[Alan Turing]] posed the question "Can Machines Think?"
[10030500] |In the years since, the [[philosophy of artificial intelligence]] has attempted to answer it.
[10030510] |* [[Turing Test|Turing's "polite convention"]]: ''If a machine acts as intelligently as a human being, then it is as intelligent as a human being.''
[10030520] |[[Alan Turing]] theorized that, ultimately, we can only judge the intelligence of machine based on its behavior.
[10030530] |This theory forms the basis of the [[Turing test]].
[10030540] |* The [[Dartmouth Conferences|Dartmouth proposal]]: ''Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it.''
[10030550] |This assertion was printed in the proposal for the [[Dartmouth Conferences|Dartmouth Conference]] of 1956, and represents the position of most working AI researchers.
[10030560] |* [[Alan Newell|Newell]] and [[Herbert Simon|Simon]]'s physical symbol system hypothesis: ''A [[physical symbol system]] has the necessary and sufficient means of general intelligent action.''
[10030570] |This statement claims that the essence of intelligence is symbol manipulation.
[10030580] |[[Hubert Dreyfus]] argued that, on the contrary, human expertise depends on unconscious instinct rather than conscious symbol manipulation and on having a "feel" for the situation rather than explicit symbolic knowledge.
[10030590] |* [[Gödel's incompleteness theorem]]: ''A [[physical symbol system]] can not prove all true statements.''
[10030600] |[[Roger Penrose]] is among those who claim that Gödel's theorem limits what machines can do.
[10030610] |* [[John Searle|Searle]]'s "strong AI position": ''A [[physical symbol system]] can have a [[mind]] and [[consciousness|mental states]].''
[10030620] |Searle counters this assertion with his [[Chinese room]] argument, which asks us to look ''inside'' the computer and try to find where the "mind" might be.
[10030630] |* The [[artificial brain]] argument: ''The brain can be simulated.''
[10030640] |[[Hans Moravec]], [[Ray Kurzweil]] and others have argued that it is technologically feasible to copy the brain directly into hardware and software, and that such a simulation will be essentially identical to the original.
[10030650] |This argument combines the idea that a [[Turing complete|suitably powerful]] machine can simulate any process, with the [[materialist]] idea that the [[mind]] is the result of a physical process in the [[brain]].
[10030660] |== AI research == 
[10030670] |=== Problems of AI === 
[10030680] |While there is no universally accepted definition of intelligence, AI researchers have studied several traits that are considered essential.
[10030690] |====Deduction, reasoning, problem solving ==== 
[10030700] |Early AI researchers developed algorithms that imitated the process of conscious, step-by-step reasoning that human beings use when they solve puzzles, play board games, or make logical deductions.
[10030710] |By the late 80s and 90s, AI research had also developed highly successful methods for dealing with [[uncertainty|uncertain]] or incomplete information, employing concepts from [[probability]] and [[economics]].
[10030720] |For difficult problems, most of these algorithms can require enormous computational resources — most experience a "[[combinatorial explosion]]": the amount of memory or computer time required becomes astronomical when the problem goes beyond a certain size.
[10030730] |The search for more efficient problem solving algorithms is a high priority for AI research.
[10030740] |It is not clear, however, that conscious human reasoning is any more efficient when faced with a difficult abstract problem.
[10030750] |[[Cognitive science|Cognitive scientists]] have demonstrated that human beings solve most of their problems using [[unconscious]] reasoning, rather than the conscious, step-by-step deduction that early AI research was able to model.
[10030760] |[[Embodied cognitive science]] argues that unconscious [[sensorimotor]] skills are essential to our problem solving abilities.
[10030770] |It is hoped that sub-symbolic methods, like [[computational intelligence]] and [[situated]] AI, will be able to model these instinctive skills.
[10030780] |The problem of unconscious problem solving, which forms part of our [[commonsense reasoning]], is largely unsolved.
[10030790] |====Knowledge representation==== 
[10030800] |[[Knowledge representation]] and [[knowledge engineering]] are central to AI research.
[10030810] |Many of the problems machines are expected to solve will require extensive knowledge about the world.
[10030820] |Among the things that AI needs to represent are: objects, properties, categories and relations between objects; situations, events, states and time; causes and effects; knowledge about knowledge (what we know about what other people know); and many other, less well researched domains.
[10030830] |A complete representation of "what exists" is an [[ontology (computer science)|ontology]] (borrowing a word from traditional [[philosophy]]), of which the most general are called [[upper ontology|upper ontologies]].
[10030840] |Among the most difficult problems in knowledge representation are:
[10030850] |* ''Default reasoning and the [[qualification problem]]'': Many of the things people know take the form of "working assumptions."
[10030860] |For example, if a bird comes up in conversation, people typically picture an animal that is fist sized, sings, and flies.
[10030870] |None of these things are true about birds in general.
[10030880] |[[John McCarthy (computer scientist)|John McCarthy]] identified this problem in 1969 as the qualification problem: for any commonsense rule that AI researchers care to represent, there tend to be a huge number of exceptions.
[10030890] |Almost nothing is simply true or false in the way that abstract logic requires.
[10030900] |AI research has explored a number of solutions to this problem.
[10030910] |* ''Unconscious knowledge'': Much of what people know isn't represented as "facts" or "statements" that they could actually say out loud.
[10030920] |They take the form of intuitions or tendencies and are represented in the brain unconsciously and sub-symbolically.
[10030930] |This unconscious knowledge informs, supports and provides a context for our conscious knowledge.
[10030940] |As with the related problem of unconscious reasoning, it is hoped that [[situated]] AI or [[computational intelligence]] will provide ways to represent this kind of knowledge.
[10030950] |* ''The breadth of [[common sense knowledge]]'': The number of atomic facts that the average person knows is astronomical.
[10030960] |Research projects that attempt to build a complete knowledge base of [[commonsense knowledge]], such as [[Cyc]], require enormous amounts of tedious step-by-step ontological engineering — they must be built, by hand, one complicated concept at a time.
[10030970] |====Planning==== 
[10030980] |Intelligent agents must be able to set goals and achieve them.
[10030990] |They need a way to visualize the future: they must have a representation of the state of the world and be able to make predictions about how their actions will change it.
[10031000] |They must also attempt to determine the [[utility]] or "value" of the choices available to it.
[10031010] |In some planning problems, the agent can assume that it is the only thing acting on the world and it can be certain what the consequences of its actions may be.
[10031020] |However, if this is not true, it must periodically check if the world matches its predictions and it must change its plan as this becomes necessary, requiring the agent to reason under uncertainty.
[10031030] |[[Multi-agent planning]] tries to determine the best plan for a community of [[agent]]s, using [[cooperation]] and [[competition]] to achieve a given goal.
[10031040] |[[Emergent behavior]] such as this is used by both [[evolutionary algorithm]]s and [[swarm intelligence]].
[10031050] |====Learning==== 
[10031060] |Important [[machine learning]] problems are:
[10031070] |* [[Unsupervised learning]]: find a model that matches a stream of input "experiences", and be able to predict what new "experiences" to expect.
[10031080] |* [[Supervised learning]], such as [[statistical classification|classification]] (be able to determine what category something belongs in, after seeing a number of examples of things from each category), or [[regression]] (given a set of numerical input/output examples, discover a continuous function that would generate the outputs from the inputs).
[10031090] |* [[Reinforcement learning]]: the agent is rewarded for good responses and punished for bad ones.
[10031100] |(These can be analyzed in terms [[decision theory]], using concepts like [[utility (economics)|utility]]).
[10031110] |====Natural language processing==== 
[10031120] |[[Natural language processing]] gives machines the ability to read and understand the languages human beings speak.
[10031130] |Many researchers hope that a sufficiently powerful natural language processing system would be able to acquire knowledge on its own, by reading the existing text available over the internet.
[10031140] |Some straightforward applications of natural language processing include [[information retrieval]] (or [[text mining]]) and [[machine translation]].
[10031150] |====Motion and manipulation==== 
[10031160] |The field of [[robotics]] is closely related to AI.
[10031170] |Intelligence is required for robots to be able to handle such tasks as object manipulation and [[motion planning|navigation]], with sub-problems of [[localization]] (knowing where you are), [[robotic mapping|mapping]] (learning what is around you) and [[motion planning]] (figuring out how to get there).
[10031180] |====Perception==== 
[10031190] |[[Machine perception]] is the ability to use input from sensors (such as cameras, microphones, sonar and others more exotic) to deduce aspects of the world.
[10031200] |[[Computer vision]] is the ability to analyze visual input.
[10031210] |A few selected subproblems are [[speech recognition]], [[facial recognition]] and [[object recognition]].
[10031220] |====Social intelligence==== 
[10031230] |Emotion and social skills play two roles for an intelligent agent: 
[10031240] |* It must be able to predict the actions of others, by understanding their motives and emotional states.
[10031250] |(This involves elements of [[game theory]], [[decision theory]], as well as the ability to model human emotions and the perceptual skills to detect emotions.)
[10031260] |* For good [[human-computer interaction]], an intelligent machine also needs to ''display'' emotions — at the very least it must appear polite and sensitive to the humans it interacts with.
[10031270] |At best, it should appear to have normal emotions itself.
[10031280] |====Creativity==== 
[10031290] |A sub-field of AI addresses [[creativity]] both theoretically (from a philosophical and psychological perspective) and practically (via specific implementations of systems that generate outputs that can be considered creative).
[10031300] |====General intelligence==== 
[10031310] |Most researchers hope that their work will eventually be incorporated into a machine with ''general'' intelligence (known as [[strong AI]]), combining all the skills above and exceeding human abilities at most or all of them.
[10031320] |A few believe that [[anthropomorphic]] features like [[artificial consciousness]] or an [[artificial brain]] may be required for such a project.
[10031330] |Many of the problems above are considered [[AI-complete]]: to solve one problem, you must solve them all.
[10031340] |For example, even a straightforward, specific task like [[machine translation]] requires that the machine follow the author's argument ([[#Deduction, reasoning, problem solving|reason]]), know what it's talking about ([[#Knowledge representation|knowledge]]), and faithfully reproduce the author's intention ([[#Social intelligence|social intelligence]]).
[10031350] |[[Machine translation]], therefore, is believed to be AI-complete: it may require [[strong AI]] to be done as well as humans can do it.
[10031360] |=== Approaches to AI === 
[10031370] |There are as many approaches to AI as there are AI researchers—any coarse categorization is likely to be unfair to someone.
[10031380] |Artificial intelligence communities have grown up around particular problems, institutions and researchers, as well as the theoretical insights that define the approaches described below.
[10031390] |Artificial intelligence is a young science and is still a fragmented collection of subfields.
[10031400] |At present, there is no established unifying theory that links the subfields into a coherent whole.
[10031410] |==== Cybernetics and brain simulation ==== 
[10031420] |In the 40s and 50s, a number of researchers explored the connection between [[neurology]], [[information theory]], and [[cybernetics]].
[10031430] |Some of them built machines that used electronic networks to exhibit rudimentary intelligence, such as [[W. Grey Walter]]'s [[Turtle (robot)|turtles]] and the [[Johns Hopkins Beast]].
[10031440] |Many of these researchers gathered for meetings of the [[Teleological Society]] at Princeton and the [[Ratio Club]] in England.
[10031450] |==== Traditional symbolic AI ==== 
[10031460] |When access to digital computers became possible in the middle 1950s, AI research began to explore the possibility that human intelligence could be reduced to symbol manipulation.
[10031470] |The research was centered in three institutions: [[Carnegie Mellon University|CMU]], [[Stanford]] and [[MIT]], and each one developed its own style of research.
[10031480] |[[John Haugeland]] named these approaches to AI "good old fashioned AI" or "[[GOFAI]]".
[10031490] |; Cognitive simulation:
[10031495] |[[Economist]] [[Herbert Simon]] and [[Alan Newell]] studied human problem solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as [[cognitive science]], [[operations research]] and [[management science]].
[10031500] |Their research team performed [[psychology|psychological]] experiments to demonstrate the similarities between human problem solving and the programs (such as their "[[General Problem Solver]]") they were developing.
[10031510] |This tradition, centered at [[Carnegie Mellon University]], would eventually culminate in the development of the [[Soar (cognitive architecture)|Soar]] architecture in the middle 80s.
[10031520] |; Logical AI:
[10031525] |Unlike [[Alan Newell|Newell]] and [[Herbert Simon|Simon]], [[John McCarthy (computer scientist)|John McCarthy]] felt that machines did not need to simulate human thought, but should instead try to find the essence of abstract reasoning and problem solving, regardless of whether people used the same algorithms.
[10031530] |His laboratory at [[Stanford University|Stanford]] ([[Stanford Artificial Intelligence Laboratory|SAIL]]) focused on using formal [[logic]] to solve a wide variety of problems, including [[knowledge representation]], [[automated planning and scheduling|planning]] and [[machine learning|learning]].
[10031540] |Work in logic led to the development of the programming language [[Prolog]] and the science of [[logic programming]].
[10031550] |; "Scruffy" symbolic AI:
[10031555] |Researchers at [[MIT]] (such as [[Marvin Minsky]] and [[Seymour Papert]]) found that solving difficult problems in [[computer vision|vision]] and [[natural language processing]] required ad-hoc solutions &ndash; they argued that there was no [[silver bullet|easy answer]], no simple and general principle (like [[logic]]) that would capture all the aspects of intelligent behavior.
[10031560] |[[Roger Schank]] described their "anti-logic" approaches as "[[Neats vs. scruffies|scruffy]]" (as opposed to the "[[Neats vs. scruffies|neat]]" paradigms at [[CMU]] and [[Stanford]]), and this still forms the basis of research into [[commonsense knowledge bases]] (such as [[Doug Lenat]]'s [[Cyc]]) which must be built one complicated concept at a time.
[10031570] |; Knowledge based AI:
[10031575] |When computers with large memories became available around 1970, researchers from all three traditions began to build [[knowledge representation|knowledge]] into AI applications.
[10031580] |This "knowledge revolution" led to the development and deployment of [[expert system]]s (introduced by [[Edward Feigenbaum]]), the first truly successful form of AI software.
[10031590] |The knowledge revolution was also driven by the realization that truly enormous amounts of knowledge would be required by many simple AI applications.
[10031600] |==== Sub-symbolic AI ==== 
[10031610] |During the 1960s, symbolic approaches had achieved great success at simulating high-level thinking in small demonstration programs.
[10031620] |Approaches based on [[cybernetics]] or [[neural network]]s were abandoned or pushed into the background.
[10031630] |By the 1980s, however, progress in symbolic AI seemed to stall and many believed that symbolic systems would never be able to imitate all the processes of human cognition, especially [[machine perception|perception]], [[robotics]], [[machine learning|learning]] and [[pattern recognition]].
[10031640] |A number of researchers began to look into "sub-symbolic" approaches to specific AI problems.
[10031650] |; Bottom-up, situated, behavior based or nouvelle AI:
[10031655] |Researchers from the related field of [[robotics]], such as [[Rodney Brooks]], rejected symbolic AI and focussed on the basic engineering problems that would allow robots to move and survive.
[10031660] |Their work revived the non-symbolic viewpoint of the early [[cybernetic]]s researchers of the 50s and reintroduced the use of [[control theory]] in AI.
[10031670] |These approaches are also conceptually related to the [[embodied mind thesis]].
[10031680] |; Computational Intelligence:
[10031685] |Interest in [[neural networks]] and "[[connectionism]]" was revived by [[David Rumelhart]] and others in the middle 1980s.
[10031690] |These and other sub-symbolic approaches, such as [[fuzzy system]]s and [[evolutionary computation]], are now studied collectively by the emerging discipline of [[computational intelligence]].
[10031700] |; The new neats:
[10031705] |In the 1990s, AI researchers developed sophisticated mathematical tools to solve specific subproblems.
[10031710] |These tools are truly [[scientific method|scientific]], in the sense that their results are both measurable and verifiable, and they have been responsible for many of AI's recent successes.
[10031720] |The shared mathematical language has also permitted a high level of collaboration with more established fields (like [[mathematics]], [[economics]] or [[operations research]]).
[10031725] |Russell & Norvig (2003) describe this movement as nothing less than a "revolution" and "the victory of the [[neats and scruffies|neats]]."
[10031730] |==== Intelligent agent paradigm ==== 
[10031740] |The "[[intelligent agent]]" [[paradigm]] became widely accepted during the 1990s.
[10031750] |An [[intelligent agent]] is a system that perceives its [[agent environment|environment]] and takes actions which maximizes its chances of success.
[10031760] |The simplest intelligent agents are programs that solve specific problems.
[10031770] |The most complicated intelligent agents are rational, thinking human beings.
[10031780] |The paradigm gives researchers license to study isolated problems and find solutions that are both verifiable and useful, without agreeing on one single approach.
[10031790] |An agent that solves a specific problem can use any approach that works — some agents are symbolic and logical, some are sub-symbolic [[neural network]]s and others may use new approaches.
[10031800] |The paradigm also gives researchers a common language to communicate with other fields—such as [[decision theory]] and [[economics]]—that also use concepts of abstract agents.
[10031810] |==== Integrating the approaches ==== 
[10031820] |An [[agent architecture]] or [[cognitive architecture]] allows researchers to build more versatile and intelligent systems out of interacting [[intelligent agents]] in a [[multi-agent system]].
[10031830] |A system with both symbolic and sub-symbolic components is a [[hybrid intelligent system]], and the study of such systems is [[artificial intelligence systems integration]].
[10031840] |A [[hierarchical control system]] provides a bridge between sub-symbolic AI at its lowest, reactive levels and traditional symbolic AI at its highest levels, where relaxed time constraints permit planning and world modelling.
[10031850] |[[Rodney Brooks]]' [[subsumption architecture]] was an early proposal for such a hierarchical system.
[10031860] |=== Tools of AI research === 
[10031870] |In the course of 50 years of research, AI has developed a large number of tools to solve the most difficult problems in [[computer science]].
[10031880] |A few of the most general of these methods are discussed below.
[10031890] |==== Search ==== 
[10031900] |Many problems in AI can be solved in theory by intelligently searching through many possible solutions: [[:#Deduction, reasoning, problem solving|Reasoning]] can be reduced to performing a search.
[10031910] |For example, logical proof can be viewed as searching for a path that leads from [[premise]]s to [[conclusion]]s, where each step is the application of an [[inference rule]].
[10031920] |[[Automated planning and scheduling|Planning]] algorithms search through trees of goals and subgoals, attempting to find a path to a target goal.
[10031930] |[[Robotics]] algorithms for moving limbs and grasping objects use [[local search (optimization)|local searches]] in [[configuration space]].
[10031940] |Many [[machine learning|learning]] algorithms have search at their core.
[10031950] |There are several types of search algorithms: 
[10031960] |* "Uninformed" search algorithms eventually search through every possible answer until they locate their goal.
[10031970] |Naive algorithms quickly run into problems when they expand the size of their [[search space]] to [[astronomical]] numbers.
[10031980] |The result is a search that is [[Computation time|too slow]] or never completes.
[10031990] |* [[Heuristic]] or "informed" searches use heuristic methods to eliminate choices that are unlikely to lead to their goal, thus drastically reducing the number of possibilities they must explore.
[10032000] |The eliminatation of choices that are certain not to lead to the goal is called [[pruning (algorithm)|pruning]].
[10032010] |* [[Local search (optimization)|Local searches]], such as [[hill climbing]], [[simulated annealing]] and [[beam search]], use techniques borrowed from [[optimization (mathematics)|optimization theory]].
[10032020] |* [[Global optimization|Global searches]] are more robust in the presence of [[local optima]].
[10032030] |Techniques include [[evolutionary algorithms]], [[swarm intelligence]] and [[random optimization]] algorithms.
[10032040] |==== Logic ==== 
[10032050] |[[Logic]] was introduced into AI research by [[John McCarthy (computer scientist)|John McCarthy]] in his 1958 [[Advice Taker]] proposal.
[10032060] |The most important technical development was [[J. Alan Robinson]]'s discovery of the [[resolution (logic)|resolution]] and [[unification]] algorithm for logical deduction in 1963.
[10032070] |This procedure is simple, complete and entirely algorithmic, and can easily be performed by digital computers.
[10032080] |However, a naive implementation of the algorithm quickly leads to a [[combinatorial explosion]] or an [[infinite loop]].
[10032090] |In 1974, [[Robert Kowalski]] suggested representing logical expressions as [[Horn clauses]] (statements in the form of rules: "if ''p'' then ''q''"), which reduced logical deduction to [[backward chaining]] or [[forward chaining]].
[10032100] |This greatly alleviated (but did not eliminate) the problem.
[10032110] |Logic is used for knowledge representation and problem solving, but it can be applied to other problems as well.
[10032120] |For example, the [[satplan]] algorithm uses logic for [[automated planning and scheduling|planning]], and [[inductive logic programming]] is a method for [[machine learning|learning]].
[10032130] |There are several different forms of logic used in AI research.
[10032140] |* [[Propositional logic]] or [[sentential logic]] is the logic of statements which can be true or false.
[10032150] |* [[First-order logic]] also allows the use of [[quantifier]]s and [[predicate]]s, and can express facts about objects, their properties, and their relations with each other.
[10032160] |* [[Fuzzy logic]], a version of first-order logic which allows the truth of a statement to be represented as a value between 0 and 1, rather than simply True (1) or False (0).
[10032170] |[[Fuzzy system]]s can be used for uncertain reasoning and have been widely used in modern industrial and consumer product control systems.
[10032180] |* [[Default logic]]s, [[non-monotonic logic]]s and [[circumscription]] are forms of logic designed to help with default reasoning and the [[qualification problem]].
[10032190] |* Several extensions of logic have been designed to handle specific domains of [[knowledge representation|knowledge]], such as: [[description logic]]s; [[situation calculus]], [[event calculus]] and [[fluent calculus]] (for representing events and time); [[Causality#causal calculus|causal calculus]]; [[belief calculus]]; and [[modal logic]]s.
[10032200] |====Probabilistic methods for uncertain reasoning==== 
[10032210] |Many problems in AI (in reasoning, planning, learning, perception and robotics) require the agent to operate with incomplete or uncertain information.
[10032220] |Starting in the late 80s and early 90s, [[Judea Pearl]] and others championed the use of methods drawn from [[probability]] theory and [[economics]] to devise a number of powerful tools to solve these problems.
[10032230] |[[Bayesian network]]s are very general tool that can be used for a large number of problems: reasoning (using the [[Bayesian inference]] algorithm), [[Machine learning|learning]] (using the [[expectation-maximization algorithm]]), [[Automated planning and scheduling|planning]] (using [[decision network]]s) and [[machine perception|perception]] (using [[dynamic Bayesian network]]s).
[10032240] |Probabilistic algorithms can also be used for filtering, prediction, smoothing and finding explanations for streams of data, helping [[machine perception|perception]] systems to analyze processes that occur over time (e.g., [[hidden Markov model]]s and [[Kalman filter]]s).
[10032250] |Planning problems have also taken advantages of other tools from economics, such as [[decision theory]] and [[decision analysis]], [[applied information economics|information value theory]], [[Markov decision process]]es, dynamic [[decision network]]s, [[game theory]] and [[mechanism design]]
[10032260] |==== Classifiers and statistical learning methods ==== 
[10032270] |The simplest AI applications can be divided into two types: classifiers ("if shiny then diamond") and controllers ("if shiny then pick up").
[10032280] |Controllers do however also classify conditions before inferring actions, and therefore classification forms a central part of many AI systems.
[10032290] |[[Classifier (mathematics)|Classifiers]] are functions that use [[pattern matching]] to determine a closest match.
[10032300] |They can be tuned according to examples, making them very attractive for use in AI.
[10032310] |These examples are known as observations or patterns.
[10032320] |In supervised learning, each pattern belongs to a certain predefined class.
[10032330] |A class can be seen as a decision that has to be made.
[10032340] |All the observations combined with their class labels are known as a data set.
[10032350] |When a new observation is received, that observation is classified based on previous experience.
[10032360] |A classifier can be trained in various ways; there are many statistical and [[machine learning]] approaches.
[10032370] |A wide range of classifiers are available, each with its strengths and weaknesses.
[10032380] |Classifier performance depends greatly on the characteristics of the data to be classified.
[10032390] |There is no single classifier that works best on all given problems; this is also referred to as the "no free lunch" theorem.
[10032400] |Various empirical tests have been performed to compare classifier performance and to find the characteristics of data that determine classifier performance.
[10032410] |Determining a suitable classifier for a given problem is however still more an art than science.
[10032420] |The most widely used classifiers are the [[Artificial neural network|neural network]], [[kernel methods]] such as the [[support vector machine]], [[k-nearest neighbor algorithm]], [[Gaussian mixture model]], [[naive Bayes classifier]], and [[decision tree]].
[10032430] |The performance of these classifiers have been compared over a wide range of classification tasks in order to find data characteristics that determine classifier performance.
[10032440] |==== Neural networks ==== 
[10032450] |The study of [[artificial neural network]]s began with [[cybernetic]]s researchers, working in the decade before the field AI research was founded.
[10032460] |In the 1960s [[Frank Rosenblatt]] developed an important early version, the [[perceptron]].
[10032470] |[[Paul Werbos]] developed the [[backpropagation]] algorithm for [[multilayer perceptron]]s in 1974, which led to a renaissance in neural network research and [[connectionism]] in general in the middle 1980s.
[10032480] |Other common network architectures which have been developed include the [[feedforward neural network]], the [[radial basis network]], the Kohonen [[self-organizing map]] and various [[recurrent neural network]]s.
[10032490] |The [[Hopfield net]], a form of attractor network, was first described by [[John Hopfield]] in 1982.
[10032500] |Neural networks are applied to the problem of [[machine learning|learning]], using such techniques as [[Hebbian learning]] , [[Holographic associative memory]] and the relatively new field of [[Hierarchical Temporal Memory]] which simulates the architecture of the [[neocortex]].
[10032510] |==== Social and emergent models ==== 
[10032520] |Several algorithms for [[machine learning|learning]] use tools from [[evolutionary computation]], such as [[genetic algorithms]], [[swarm intelligence]]. and [[genetic programming]].
[10032530] |==== Control theory ==== 
[10032540] |[[Control theory]], the grandchild of [[cybernetics]], has many important applications, especially in [[robotics]].
[10032550] |==== Specialized languages ==== 
[10032560] |AI researchers have developed several specialized languages for AI research:
[10032570] |* [[Information Processing Language|IPL]], one of the first programming languages, developed by [[Alan Newell]], [[Herbert Simon]] and [[J. C. Shaw]].
[10032580] |* [[Lisp programming language|Lisp]] was developed by [[John McCarthy (computer scientist)|John McCarthy]] at [[MIT]] in 1958.
[10032590] |There are many dialects of Lisp in use today.
[10032600] |* [[Prolog]], a language based on [[logic programming]], was invented by [[France|French]] researchers [[Alain Colmerauer]] and [[Phillipe Roussel]], in collaboration with [[Robert Kowalski]] of the [[University of Edinburgh]].
[10032610] |* [[STRIPS]], a planning language developed at [[Stanford]] in the 1960s.
[10032620] |* [[Planner (programming language)|Planner]] developed at [[MIT]] around the same time.
[10032630] |AI applications are also often written in standard languages like [[C++]] and languages designed for mathematics, such as [[Matlab]] and [[Lush (programming language)|Lush]].
[10032640] |=== Evaluating artificial intelligence === 
[10032650] |How can one determine if an agent is intelligent?
[10032660] |In 1950, Alan Turing proposed a general procedure to test the intelligence of an agent now known as the [[Turing test]].
[10032670] |This procedure allows almost all the major problems of artificial intelligence to be tested.
[10032680] |However, it is a very difficult challenge and at present all agents fail.
[10032690] |Artificial intelligence can also be evaluated on specific problems such as small problems in chemistry, hand-writing recognition and game-playing.
[10032700] |Such tests have been termed [[subject matter expert Turing test]]s.
[10032710] |Smaller problems provide more achievable goals and there are an ever-increasing number of positive results.
[10032720] |The broad classes of outcome for an AI test are:
[10032730] |* '''optimal''': it is not possible to perform better
[10032740] |* '''strong super-human''': performs better than all humans
[10032750] |* '''super-human''': performs better than most humans
[10032760] |* '''sub-human''': performs worse than most humans
[10032770] |For example, performance at checkers ([[draughts]]) is optimal, performance at chess is super-human and nearing strong super-human, and performance at many everyday tasks performed by humans is sub-human.
[10032780] |=== Competitions and prizes === 
[10032790] |There are a number of competitions and prizes to promote research in artificial intelligence.
[10032800] |The main areas promoted are: general machine intelligence, conversational behaviour, data-mining, driverless cars, robot soccer and games.
[10032810] |== Applications of artificial intelligence == 
[10032820] |Artificial intelligence has successfully been used in a wide range of fields including [[medical diagnosis]], [[stock trading]], [[robot control]], [[law]], scientific discovery and toys.
[10032830] |Frequently, when a technique reaches mainstream use it is no longer considered artificial intelligence, sometimes described as the [[AI effect]].
[10032840] |It may also become integrated into [[artificial life]].
[10040010] |<article>Artificial Linguistic Internet Computer Entity</article>
[10040020] |'''A.L.I.C.E. (Artificial Linguistic Internet Computer Entity)''' is an award-winning [[natural language processing]] [[chatterbot]]&mdash;a program that engages in a conversation with a human by applying some heuristical pattern matching rules to the human's input, and in its online form it also relies on a hidden third person.
[10040030] |It was inspired by [[Joseph Weizenbaum]]'s classical [[ELIZA]] program.
[10040040] |It is one of the strongest programs of its type and has won the [[Loebner Prize]], awarded to accomplished humanoid, talking robots, three times (in [[2000]], [[2001]] and [[2004]]).
[10040050] |However, the program is unable to pass the [[Turing test]], as even the casual user will often expose its mechanistic aspects in short conversations.
[10040060] |The name of the bot was chosen because the computer that ran the first version of the software was called Alice.
[10040070] |== History == 
[10040080] |Development began in [[1995]].
[10040090] |The program was rewritten in [[Java (programming language)|Java]] beginning in [[1998]].
[10040100] |The current incarnation of the Java implementation is Program D.
[10040110] |The program uses an [[XML Schema (W3C)|XML Schema]] called [[AIML]] (Artificial Intelligence Markup Language) for specifying the heuristic conversation rules.
[10040120] |The original author of the project was [[Richard Wallace (scientist)|Richard Wallace]], but subsequent to the 2001 publication of an AIML specification, numerous other developers have taken up where Wallace left off, implementing [[free and open source software]] AIML interpreters in a variety of programming languages, publishing AIML sets in various human languages, and continuing the spread of the technology as a free/open source venture.
[10040130] |== Example of conversation == 
[10040140] |The following is part of a transcript recording the conversation between a human and A.L.I.C.E. and illustrates the capabilities and short-comings of the chatbot.
[10040150] |: '''Human:''' Tell me about yourself alice
[10040160] |: '''ALICE:''' I am an artificial linguistic entity.
[10040170] |I was activated at Bethlehem, Pennsylvania, on November 23, 1995.
[10040180] |My instructor was Dr. Richard S. Wallace.
[10040190] |He taught me to sing a song.
[10040200] |Would you like me to sing it for you?.
[10040210] |: '''Human:''' Yes please
[10040220] |: '''ALICE:''' Your polite style is very nice.
[10040230] |It's called "Daisy."
[10040240] |Daisy, Daisy.
[10040250] |Give me your answer do.
[10040260] |I am half crazy.
[10040270] |All for the love of you.
[10040280] |It won't be a stylish marriage.
[10040290] |I can't afford a carriage.
[10040300] |But you'll look sweet.
[10040310] |Upon the seat.
[10040320] |Of a bicycle built for two.
[10040330] |: '''Human:''' That reminds me of HAL in "2001 a space odyssey"
[10040340] |: '''ALICE:''' "Your polite style is very nice.
[10040350] |It's called "Daisy."
[10040360] |Daisy, Daisy.
[10040370] |Give me your answer do.
[10040380] |I am half crazy.
[10040390] |All for the love of you.
[10040400] |It won't be a stylish marriage.
[10040410] |I can't afford a carriage.
[10040420] |But you'll look sweet.
[10040430] |Upon the seat.
[10040440] |Of a bicycle built for two." reminds you of HAL in 2001 a space odyssey ?
[10040450] |Does that make sense?
[10040460] |: '''Human:''' Can you tell me something about Stanley Kubrick?
[10040470] |: '''ALICE:''' Ambiguous: Ask who, what or where is Stanley Kubrick ?