Two particularly active branches of research in constraint satisfaction are the study of promise constraint satisfaction problems (PCSPs) with finite templates and the study of infinite-domain constraint satisfaction problems with ω-categorical templates. In this paper, we explore some connections between these two hitherto unrelated fields and describe a general approach to studying the complexity of PCSPs by constructing suitable infinite CSP templates. As a result, we obtain new characterizations of the power of various classes of algorithms for PCSPs, such as first-order logic, arc consistency reductions, and obtain new proofs of the characterizations of the power of the classical linear and affine relaxations for PCSPs.
@InProceedings{mottet:LIPIcs.CSL.2024.41, author = {Mottet, Antoine}, title = {{Promise and Infinite-Domain Constraint Satisfaction}}, booktitle = {32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)}, pages = {41:1--41:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-310-2}, ISSN = {1868-8969}, year = {2024}, volume = {288}, editor = {Murano, Aniello and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.41}, URN = {urn:nbn:de:0030-drops-196842}, doi = {10.4230/LIPIcs.CSL.2024.41}, annote = {Keywords: promise constraint satisfaction problems, polymorphisms, homogeneous structures, first-order logic} }
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