Complexity of Existential Positive First-Order Logic

Authors:
Manuel Bodirsky;Miki Hermann;Florian Richoux
Affiliations:
LIX (CNRS, UMR 7161), École Polytechnique, Palaiseau, France 91128;LIX (CNRS, UMR 7161), École Polytechnique, Palaiseau, France 91128;LIX (CNRS, UMR 7161), École Polytechnique, Palaiseau, France 91128
Venue:
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Year:
2009

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Abstract

Let Γ be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in Γ is in LOGSPACE or complete for the class CSP(Γ)NP under deterministic polynomial-time many-one reductions. Here, CSP(Γ)NP is the class of problems that can be reduced to the constraint satisfaction problem of Γ under non-deterministic polynomial-time many-one reductions.