Boolean symmetric vs. functional PCSP dichotomy

As our first result, we establish a dichotomy for promise constraint satisfaction problems of the form PCSP(A, B), where A is Boolean and symmetric and B is functional (on a domain of any size); i.e, all but one element of any tuple in a relation in B determine the last element. This includes PCSPs...

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Bibliographic Details
Published in2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) pp. 1 - 12
Main Authors Nakajima, Tamio-Vesa, Zivny, Stanislav
Format Conference Proceeding
LanguageEnglish
Published IEEE 26.06.2023
Subjects
algebraic approach
Complexity theory
Computer science
constraint satisfaction
dichotomy
Integer programming
minions
polymorphisms
promise CSP
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DOI10.1109/LICS56636.2023.10175746

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Summary:As our first result, we establish a dichotomy for promise constraint satisfaction problems of the form PCSP(A, B), where A is Boolean and symmetric and B is functional (on a domain of any size); i.e, all but one element of any tuple in a relation in B determine the last element. This includes PCSPs of the form PCSP(q-in-r, B), where B is functional, thus making progress towards a classification of PCSP(1-in-3, B), which were studied by Barto, Battistelli, and Berg [STACS'21] for B on three-element domains.As our second result, we show that for PCSP(A, B), where A contains a single symmetric relation and B is arbitrary (and thus not necessarily functional), the combined basic linear programming relaxation (BLP) and the affine integer programming relaxation (AIP) of Brakensiek et al. [SICOMP'20] is no more powerful than the (in general strictly weaker) AIP relaxation of Brakensiek and Guruswami [SICOMP'21].
DOI:10.1109/LICS56636.2023.10175746