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arXiv · 2012.05682

Tractable Combinations of Temporal CSPs

Manuel Bodirsky·Johannes Greiner·Jakub Rydval
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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$(Q;<)$.

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BibTeXRIS

Manuel Bodirsky, Johannes Greiner, Jakub Rydval. 2020-12-10. Tractable Combinations of Temporal CSPs. https://doi.org/10.46298/lmcs-18(2%3A11)2022

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