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DOI: 10.4230/LIPIcs.CSL.2018.18
URN: urn:nbn:de:0030-drops-96851
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9685/
Das, Anupam ; Oitavem, Isabel
A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions
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Abstract
We extend work of Lautemann, Schwentick and Stewart [Clemens Lautemann et al., 1996] on characterisations of the "positive" polynomial-time predicates (posP, also called mP by Grigni and Sipser [Grigni and Sipser, 1992]) to function classes. Our main result is the obtention of a function algebra for the positive polynomial-time functions (posFP) by imposing a simple uniformity constraint on the bounded recursion operator in Cobham's characterisation of FP. We show that a similar constraint on a function algebra based on safe recursion, in the style of Bellantoni and Cook [Stephen Bellantoni and Stephen A. Cook, 1992], yields an "implicit" characterisation of posFP, mentioning neither explicit bounds nor explicit monotonicity constraints.
BibTeX - Entry
@InProceedings{das_et_al:LIPIcs:2018:9685,
author = {Anupam Das and Isabel Oitavem},
title = {{A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions}},
booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
pages = {18:1--18:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-088-0},
ISSN = {1868-8969},
year = {2018},
volume = {119},
editor = {Dan Ghica and Achim Jung},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9685},
URN = {urn:nbn:de:0030-drops-96851},
doi = {10.4230/LIPIcs.CSL.2018.18},
annote = {Keywords: Monotone complexity, Positive complexity, Function classes, Function algebras, Recursion-theoretic characterisations, Implicit complexity, Logic}
}
| Keywords: | Monotone complexity, Positive complexity, Function classes, Function algebras, Recursion-theoretic characterisations, Implicit complexity, Logic | |
| Seminar: | 27th EACSL Annual Conference on Computer Science Logic (CSL 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 29.08.2018 |
