Partial Recursive Function And Turing - Latest Information & Updates 2026

Web Reference: Theorem 4.4.1 Every RAM-computable function is Turing-computable. Fur-thermore, given a RAM program P , we can effectively construct a Turing machine M computing the same function. In the equivalence of models of computability, a parallel is drawn between Turing machines that do not terminate for certain inputs and an undefined result for that input in the corresponding partial recursive function. A partial function is called partial recursive if it can be computed by a Turing machine; that is, if there exists a Turing machine that accepts input x exactly when f (x) is defined, in which case it leaves the string f (x) on its tape upon acceptance.

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