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URN: urn:nbn:de:0030-drops-96851
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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: 2018


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