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- W2941546582 abstract "A PCSP is a combination of two CSPs defined by two similar templates; the computational question is to distinguish a YES instance of the first one from a NO instance of the second. The computational complexity of many PCSPs remains unknown. Even the case of Boolean templates (solved for CSP by Schaefer [STOC'78]) remains wide open. The main result of Brakensiek and Guruswami [SODA'18] shows that Boolean PCSPs exhibit a dichotomy (PTIME vs. NPC) when the clauses are and for of variables''. In this paper we remove the allow for of variables'' assumption from the theorem. The symmetric assumption means that changing the order of in a constraint does not change its satisfiability. The negation of variables means that both of the templates share a relation which can be used to effectively negate Boolean variables. The main result of this paper establishes dichotomy for all the boolean templates. The tractability case of our theorem and the theorem of Brakensiek and Guruswami are almost identical. The main difference, and the main contribution of this work, is the new reason for hardness and the reasoning proving the split." @default.
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- W2941546582 date "2019-04-29" @default.
- W2941546582 modified "2023-09-27" @default.
- W2941546582 title "Dichotomy for symmetric Boolean PCSPs" @default.
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