Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case

Libor Barto; Diego Battistelli; Kevin M. Berg

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arXiv · 2010.04623

Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case

Libor Barto·Diego Battistelli·Kevin M. Berg

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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."

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Libor Barto, Diego Battistelli, Kevin M. Berg. 2020-10-09. Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case. https://arxiv.org/abs/2010.04623

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