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(1) A rule or procedure for solving a recurrent
mathematical problem. (2) A complete, unambiguous procedure for
solving a specified problem in a finite number of steps.
(Richard Dorf) (3) Deterministic algorithm: Given the same
input information, will always produce the same output
information, when applied correctly. (John Warfield) (4)
Stochastic algorithm: Given the same information, will not
necessarily produce the same output information, even though
applied correctly. (John Warfield) (5) Any mechanical or
recursive computational procedure (Dictionary).
An explicit procedure for performing a complex operation by carrying out a precisely determined and finite sequence of simple operations. E.g., the multiplication of large numbers in small steps involving only single-digit multiplications and additions, the detailed instruction for assembling a piece of electronic equipment from components, a recipe. Algorithms can vary greatly in complexity and there are usually more than one for reaching a desired end. Algorithms have greatly enhanced the human capacity for performing complex intellectual tasks by organizing detailed plans, scripts and procedures hierarchically (see hierarchy). Algorithms are also built into formal social organizations which are geared to achieve particular ends. Finally, algorithms are the subject of all computer programs and the object of higher order programming LANGUAGEs. Algorithms leave nothing undefined and require no intuition to achieve their end. (Krippendorff)