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- W4383860462 abstract "Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise, it is NP-complete. In this paper, we analyze boolean CSPs in terms of their topological complexity, instead of their computational complexity. We attach a natural topological space to the set of solutions of a boolean CSP and introduce the notion of projection-universality. We prove that a boolean CSP is projection-universal if and only if it is categorized as NP-complete by Schaefer's dichotomy theorem, showing that the dichotomy translates exactly from computational to topological complexity. We show a similar dichotomy for SAT variants and homotopy-universality." @default.
- W4383860462 created "2023-07-11" @default.
- W4383860462 creator A5000735637 @default.
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- W4383860462 date "2023-07-07" @default.
- W4383860462 modified "2023-09-27" @default.
- W4383860462 title "A Topological Version of Schaefer's Dichotomy Theorem" @default.
- W4383860462 doi "https://doi.org/10.48550/arxiv.2307.03446" @default.
- W4383860462 hasPublicationYear "2023" @default.
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