Algebraic Approach to Promise Constraint Satisfaction

نویسندگان

چکیده

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over past 20 years. A new version CSP, promise CSP (PCSP), recently proposed, motivated by open questions about variants satisfiability graph colouring. PCSP significantly extends standard decision CSP. CSPs with a fixed language on finite domain fully classified, greatly guided algebraic approach, which uses polymorphisms—high-dimensional symmetries solution spaces—to analyse problems. corresponding classification for PCSPs is wide includes some long-standing questions, such as approximate colouring, special cases. basic approach to was initiated Brakensiek Guruswami, in this article, we extend it lift from concrete properties polymorphisms their abstract properties. We introduce class problems that can be viewed versions (Gap) Label Cover show every equivalent form. This allows us identify “measure symmetry” well suited comparing relating different via approach. demonstrate how our theory applied giving both general specific hardness/tractability results. Among other things, improve state-of-the-art colouring showing that, any k ≥ 3, NP-hard find (2 -1)-colouring given -colourable graph.

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ژورنال

عنوان ژورنال: Journal of the ACM

سال: 2021

ISSN: ['0004-5411', '1557-735X']

DOI: https://doi.org/10.1145/3457606