2 Search Results for "Lautemann, Clemens"


Document
A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions

Authors: Anupam Das and Isabel Oitavem

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)


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.

Cite as

Anupam Das and Isabel Oitavem. A Recursion-Theoretic Characterisation of the Positive Polynomial-Time Functions. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{das_et_al:LIPIcs.CSL.2018.18,
  author =	{Das, Anupam and Oitavem, Isabel},
  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 =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.18},
  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}
}
Document
Counting Results in Weak Formalisms

Authors: Arnaud Durand, Clemens Lautemann, and Malika More

Published in: Dagstuhl Seminar Proceedings, Volume 6451, Circuits, Logic, and Games (2007)


Abstract
The counting ability of weak formalisms is of interest as a measure of their expressive power. The question was investigated in the 1980's in several papers in complexity theory and in weak arithmetic. In each case, the considered formalism (AC$^0$--circuits, first--order logic, $Delta_0$, respectively) was shown to be able to count precisely up to a polylogarithmic number. An essential part of each of the proofs is the construction of a 1--1 mapping from a small subset of ${0,ldots,N-1}$ into a small initial segment. In each case the expressibility of such a mapping depends on some strong argument (group theoretic device or prime number theorem) or intricate construction. We present a coding device based on a collision-free hashing technique, leading to a completely elementary proof for the polylog counting capability of first--order logic (with built--in arithmetic), $AC^0$--circuits, rudimentary arithmetic, the Linear Hierarchy, and monadic--second order logic with addition.

Cite as

Arnaud Durand, Clemens Lautemann, and Malika More. Counting Results in Weak Formalisms. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 6451, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


Copy BibTex To Clipboard

@InProceedings{durand_et_al:DagSemProc.06451.4,
  author =	{Durand, Arnaud and Lautemann, Clemens and More, Malika},
  title =	{{Counting Results in Weak Formalisms}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6451},
  editor =	{Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06451.4},
  URN =		{urn:nbn:de:0030-drops-9767},
  doi =		{10.4230/DagSemProc.06451.4},
  annote =	{Keywords: Small complexity classes, logic, polylog counting}
}
  • Refine by Author
  • 1 Das, Anupam
  • 1 Durand, Arnaud
  • 1 Lautemann, Clemens
  • 1 More, Malika
  • 1 Oitavem, Isabel

  • Refine by Classification
  • 1 Theory of computation → Recursive functions

  • Refine by Keyword
  • 1 Function algebras
  • 1 Function classes
  • 1 Implicit complexity
  • 1 Logic
  • 1 Monotone complexity
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2007
  • 1 2018

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail