The Equivalence of Turing-Computability and μ-Recursiveness
We have already emphasized in the preface that the equivalence of the suggested precise replacements of the intuitive concept of computable function can be shown by purely mathematical considerations. We shall do this in this chapter for the concept of Turing-computable function and the concept of μ-recursive function. (Cf. also Chapter 5 and § 30.) An equivalence proof of this kind generally leads to a standard representation of computable functions. Thus, we shall obtain (in § 18) Kleene’s normal form theorem.
KeywordsTuring Machine Regular Function Recursive Function Computable Function Inductive Definition
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