License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09441.4
URN: urn:nbn:de:0030-drops-23680
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2368/
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Willard, Ross

PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

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09441.WillardRoss.Paper.2368.pdf (0.2 MB)

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:DagSemProc.09441.4,
  author =	{Willard, Ross},
  title =	{{PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2010/2368},
  URN =		{urn:nbn:de:0030-drops-23680},
  doi =		{10.4230/DagSemProc.09441.4},
  annote =	{Keywords: Primitive positive formula, definability, complexity}
}

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

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