# algorithm

Ask AI3: What is algorithm?

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## Sentences

A moment's reflection shows that the above

**algorithm**and presentation work equally well in this case.
Flow chart of an

**algorithm**( Euclid's**algorithm**) for calculating the greatest common divisor ( g. c. d.
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 ).
In mathematics and computer science, an

**algorithm**( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.
More precisely, an

**algorithm**is an effective method expressed as a finite list of well-defined instructions for calculating a function.
: For a detailed presentation of the various points of view around the definition of "

**algorithm**" see Algorithm characterizations.
While there is no generally accepted formal definition of "

**algorithm**," an informal definition could be " a set of rules that precisely defines a sequence of operations.
" For some people, a program is only an

**algorithm**if it stops eventually ; for others, a program is only an**algorithm**if it stops before a given number of calculation steps.
A prototypical example of an

**algorithm**is Euclid's**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.
" 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.
In logic, the time that an

**algorithm**requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.
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.
Thus, an

**algorithm**can be considered to be any sequence of operations that can be simulated by a Turing-complete system.
Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every

**algorithm**can be simulated by a Turing machine ... according to Savage, an**algorithm**is a computational process defined by a Turing machine ".
Typically, when an

**algorithm**is associated with processing information, data is read from an input source, written to an output device, and / or stored for further processing.
For some such computational process, the

**algorithm**must be rigorously defined: specified in the way it applies in all possible circumstances that could arise.
Because an

**algorithm**is a precise list of precise steps, the order of computation will always be critical to the functioning of the**algorithm**.
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