License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.108
URN: urn:nbn:de:0030-drops-62435
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6243/
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Hoyrup, Mathieu

The Decidable Properties of Subrecursive Functions

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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.

BibTeX - Entry

@InProceedings{hoyrup:LIPIcs:2016:6243,
  author =	{Mathieu Hoyrup},
  title =	{{The Decidable Properties of Subrecursive Functions}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{108:1--108:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6243},
  URN =		{urn:nbn:de:0030-drops-62435},
  doi =		{10.4230/LIPIcs.ICALP.2016.108},
  annote =	{Keywords: Rice theorem, subrecursive class, decidable property, Kolmogorov complexity, compressibility}
}

Keywords: Rice theorem, subrecursive class, decidable property, Kolmogorov complexity, compressibility
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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