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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.
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.
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).
Thus an algorithm can be an algebraic equation such as y = m n – two arbitrary "input variables" m and n that produce an output y.
But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example): The concept of algorithm is also used to define the notion of decidability.
About 825, he wrote a treatise in the Arabic language, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum.
This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules.