{"type":"ScholarlyArticle","title":"Lower Bounds and Faster Algorithms for Equality Constraints","authors":[{"name":"Peter Jonsson","slug":"peter-jonsson","given":"Peter","family":"Jonsson","affiliation":"Department of Computer and Information Science , Linköping University , Linköping , Sweden"},{"name":"Victor Lagerkvist","slug":"victor-lagerkvist","given":"Victor","family":"Lagerkvist","affiliation":"Department of Computer and Information Science , Linköping University , Linköping , Sweden"}],"abstract":"We study the fine-grained complexity of NP-complete, infinite-domain constraint satisfaction problems (CSPs) parameterised by a set of first-order definable relations (with equality). Such CSPs are of central importance since they form a subclass of any infinite-domain CSP parameterised by a set of first-order definable relations. We prove that under the randomised exponential-time hypothesis it is not possible to find c > 1 such that a CSP over an arbitrary finite equality language is solvable in O(c^n) time (n is the number of variables). Stronger lower bounds are possible for infinite equality languages where we rule out the existence of 2^o(n log n) time algorithms; a lower bound which also extends to satisfiability modulo theories solving for an arbitrary background theory. Despite these lower bounds we prove that for each c > 1 there exists an NP-hard equality CSP solvable in O(c^n) time. Lower bounds like these immediately ask for closely matching upper bounds, and we prove that a CSP over a finite equality language is always solvable in O(c^n) time for a fixed c.","doi":"10.24963/ijcai.2020/247","url":"https://ijcai.org/proceedings/2020/247","pdf":"https://ijcai.org/proceedings/2020/0247.pdf","markdown":"https://ijcai.org/proceedings/2020/247.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/247","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":247,"pages":{"first":1784,"last":1790},"keywords":["Constraints and SAT: Satisfiability Modulo Theories","Constraints and SAT: Constraint Satisfaction","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25044/file_25044.m3u8","length_sec":264,"provider":"hls"}],"references":[{"position":1,"raw":"[Barto and Pinsker, 2016] L. 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