Tractable Combinations of Temporal CSPs
Manuel Bodirsky, Johannes Greiner, Jakub Rydval

TL;DR
This paper investigates the computational complexity of combined temporal constraint satisfaction problems, showing they are either efficiently solvable or NP-complete, based on algebraic properties of temporal structures.
Contribution
It characterizes the complexity of CSPs formed by combining two temporal theories, establishing a dichotomy in their computational complexity.
Findings
CSP$(T_1 up T_2)$ is either in P or NP-complete.
The complexity depends on algebraic properties of the structures involved.
A purely algebraic proof relates to the lattice of clones over $Q$.
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 where and are theories with disjoint finite relational signatures. We prove that if and are the theories of temporal structures, i.e., structures where all relations have a first-order definition in , then CSP 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 that contain Aut.
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Taxonomy
TopicsConstraint Satisfaction and Optimization
