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Finitely Tractable Promise Constraint Satisfaction Problems

Authors Kristina Asimi, Libor Barto

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Kristina Asimi
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czechia
Libor Barto
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czechia

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Kristina Asimi and Libor Barto. Finitely Tractable Promise Constraint Satisfaction Problems. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 11:1-11:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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].

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Constraint and logic programming
  • Constraint satisfaction problems
  • promise constraint satisfaction
  • Boolean PCSP
  • polymorphism
  • finite tractability
  • homomorphic relaxation


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