Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case

Authors Libor Barto , Diego Battistelli, Kevin M. Berg



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Author Details

Libor Barto
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Diego Battistelli
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Kevin M. Berg
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

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Libor Barto, Diego Battistelli, and Kevin M. Berg. Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.10

Abstract

The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases - approximation variants of satisfiability and graph coloring problems. We give an almost complete classification for the class of PCSPs of the form: given a 3-uniform hypergraph that has an admissible 2-coloring, find an admissible 3-coloring, where admissibility is given by a ternary symmetric relation. The only PCSP of this sort whose complexity is left open in this work is a natural hypergraph coloring problem, where admissibility is given by the relation "if two colors are equal, then the remaining one is higher."

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • constraint satisfaction problems
  • promise constraint satisfaction
  • Boolean PCSP
  • polymorphism

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References

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