Tractable Combinations of Temporal CSPs
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Published:2022-05-25
Issue:
Volume:Volume 18, Issue 2
Page:
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ISSN:1860-5974
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Container-title:Logical Methods in Computer Science
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language:en
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Short-container-title:
Author:
Bodirsky Manuel,Greiner Johannes,Rydval Jakub
Abstract
The constraint satisfaction problem (CSP) of a first-order theory T is the
computational problem of deciding whether a given conjunction of atomic
formulas is satisfiable in some model of T. We study the computational
complexity of CSP$(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with
disjoint finite relational signatures. We prove that if $T_1$ and $T_2$ are the
theories of temporal structures, i.e., structures where all relations have a
first-order definition in $(Q;<)$, then CSP$(T_1 \cup T_2)$ is in P or
NP-complete. To this end we prove a purely algebraic statement about the
structure of the lattice of locally closed clones over the domain $Q$ that
contain Aut$(Q;<)$.
Funder
European Commission
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
General Computer Science,Theoretical Computer Science