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URN: urn:nbn:de:0030-drops-23680
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2368/
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Willard, Ross

PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

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Abstract

$exists$-InvSat is the problem which takes as input a relation $R$ and a finite set $mathcal S$ of relations on the same finite domain $D$, and asks whether $R$ is definable by a conjunctive query over $mathcal S$, i.e., by a formula of the form $exists mathbf{y} varphi(mathbf{x},mathbf{y})$ where $varphi$ is a conjunction of atomic formulas built on the relations in $mathcal S cup {=}$. (These are also called emph{primitive positive formulas}.) The problem is known to be in co-NExpTime, and has been shown to be tractable on the boolean domain. We show that there exists $k>2$ such that $exists$-InvSat is co-NExpTime complete on $k$-element domains, answering a question of Creignou, Kolaitis and Zanuttini.

BibTeX - Entry

@InProceedings{willard:DSP:2010:2368,
  author =	{Ross Willard},
  title =	{PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  year =	{2010},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  number =	{09441},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2368},
  annote =	{Keywords: Primitive positive formula, definability, complexity}
}

Keywords: Primitive positive formula, definability, complexity
Seminar: 09441 - The Constraint Satisfaction Problem: Complexity and Approximability
Issue Date: 2010
Date of publication: 07.01.2010


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