Abstract
The objective of this chapter is to obtain mathematical definitions for the class of computable functions and decidable problems. The class of recursive functions is first considered and we prove that it coincides with the class of functions computable by a Turing machine. Other characterizations are given: recursive systems and functions represented by a term of the lambda-calculus. What is fundamental is that all these different definitions are equivalent, as they characterize the same class of functions.
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© 2004 Springer-Verlag London
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Lassaigne, R., de Rougemont, M. (2004). Recursion and decidability. In: Logic and Complexity. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-0-85729-392-3_7
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DOI: https://doi.org/10.1007/978-0-85729-392-3_7
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1052-1
Online ISBN: 978-0-85729-392-3
eBook Packages: Springer Book Archive