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DOI: 10.4230/LIPIcs.ICALP.2016.108
URN: urn:nbn:de:0030-drops-62435
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6243/
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 | |
| Seminar: | 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 23.08.2016 |
