DagSemProc.09441.4.pdf
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PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE
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Dagstuhl Seminar Proceedings, Volume 9441
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
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- Publication Date: 2010-01-07
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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
https://doi.org/10.4230/DagSemProc.09441.4
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.
Keywords
- Primitive positive formula
- definability
- complexity
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