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An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminates at some point. Specific algorithms are sometimes called a method, a procedure, or a technique. The word algorithm is a distortion of al-Khwarizmi, a Persian mathematician who wrote an influential treatise about algebraic methods. The process of applying an algorithm to an input to obtain an output is called a computation.

Clearly, each Turing machineconstitutes an algorithm in the intuitive sense. The statement that a Turing machine is a general-enough mathematical model for the intuitive notion of an algorithm is usually referred to as Church's thesis.