Finitely (In)tractable Promise Constraint Satisfaction Problems

Kristina Asimi; Libor Barto

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arXiv · 2010.04618

Finitely (In)tractable Promise Constraint Satisfaction Problems

Kristina Asimi·Libor Barto

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Abstract

The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a specific PCSP, the problem to find a valid Not-All-Equal solution to a 1-in-3-SAT instance, is not finitely tractable in that it can be solved by a trivial reduction to a tractable CSP, but such a CSP is necessarily over an infinite domain (unless P=NP). We initiate a systematic study of this phenomenon by giving a general necessary condition for finite tractability and characterizing finite tractability within a class of templates - the "basic" tractable cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami [SODA'18].

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Kristina Asimi, Libor Barto. 2020-10-09. Finitely (In)tractable Promise Constraint Satisfaction Problems. https://arxiv.org/abs/2010.04618

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