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The Decidable Properties of Subrecursive Functions

Author Mathieu Hoyrup

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Mathieu Hoyrup

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Mathieu Hoyrup. The Decidable Properties of Subrecursive Functions. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 108:1-108:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.108

Abstract

What can be decided or semidecided about a primitive recursive function, given a definition of that function by primitive recursion? What about subrecursive classes other than primitive recursive functions? We provide a complete and explicit characterization of the decidable and semidecidable properties. This characterization uses a variant of Kolmogorov complexity where only programs in a subrecursive programming language are allowed. More precisely, we prove that all the decidable and semidecidable properties can be obtained as combinations of two classes of basic decidable properties: (i) the function takes some particular values on a finite set of inputs, and (ii) every finite part of the function can be compressed to some extent.

Subject Classification

Keywords
  • Rice theorem
  • subrecursive class
  • decidable property
  • Kolmogorov complexity
  • compressibility

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