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Similarly, IF A -gə-ridh-əm) is an unambiguous specification of how to solve a class of problems.Algorithms can perform calculation, data processing and automated reasoning tasks.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.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.It begins thus: A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flow chart above and as an example in a later section.Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation.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. according to Savage [1987], an algorithm is a computational process defined by a Turing machine".

The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b).Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, drakon-charts, programming languages or control tables (processed by interpreters).Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms.Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Stored data are regarded as part of the internal state of the entity performing the algorithm.Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. that any procedure which could "naturally" be called effective, can in fact be realized by a (simple) machine. In practice, the state is stored in one or more data structures.