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Recursion Theory

Iain Phillips

Open publisher page 5 citations

Abstract

Abstract Computability theory might be a better name for recursion theory, since it is the mathematical study of what is computable. However the name is traditional. It arose because recursion theory started as the study of the recursive functions, a mathematical characterization of the functions which are computable (by some program). ‘Recursive’ because, just as in most programming languages, recursion is an important and very powerful mechanism for constructing these functions.

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What this paper is about

Abstract Computability theory might be a better name for recursion theory, since it is the mathematical study of what is computable. However the name is traditional. It arose because recursion theory started as the study of the recursive functions, a mathematical characterization of the functions which are computable (by some program). ‘Recursive’ because, just as in most programming languages, recursion is an important and very powerful mechanism for constructing these functions.

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Available abstract

Abstract Computability theory might be a better name for recursion theory, since it is the mathematical study of what is computable. However the name is traditional. It arose because recursion theory started as the study of the recursive functions, a mathematical characterization of the functions which are computable (by some program). ‘Recursive’ because, just as in most programming languages, recursion is an important and very powerful mechanism for constructing these functions.

Key concepts: Computability theory, Recursion (computer science), Computable function, Double recursion, Mutual recursion, Primitive recursive function, Computability, Algebra over a field

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