So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming.This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means.Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B.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).That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules.In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ...Authors who assert this thesis include Minsky (1967), Savage (1987) and Gurevich (2000): Minsky: "But we will also maintain, with Turing . For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise.That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).
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 flow of control.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.'arithmetic'), the Latin word was altered to algorithmus, and the corresponding English term 'algorithm' is first attested in the 17th century; the modern sense was introduced in the 19th century.In English, it was first used in about 1230 and then by Chaucer in 1391.English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English.