PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

Willard, Ross

doi:10.4230/DagSemProc.09441.4

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PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

Author Ross Willard

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 9441
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2010-01-07

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DagSemProc.09441.4.pdf

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DOI: 10.4230/DagSemProc.09441.4
URN: urn:nbn:de:0030-drops-23680

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Keywords

Primitive positive formula
definability
complexity

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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.

Cite As Get BibTex

Ross Willard. PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/DagSemProc.09441.4

Author Details

Ross Willard

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