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PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

Author Ross Willard



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DagSemProc.09441.4.pdf
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Ross Willard

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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

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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