research-article

Temporal Constraint Satisfaction Problems in Fixed-Point Logic

Authors:

Manuel Bodirsky,

Jakub RydvalAuthors Info & Claims

LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

Pages 237 - 251

https://doi.org/10.1145/3373718.3394750

Published: 08 July 2020 Publication History

Abstract

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes can be described by a strong height-one Maltsev condition. For infinite-domain CSPs, the situation is more complicated even if the template structure of the CSP is model-theoretically tame. We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (Q; <); such CSPs are called temporal CSPs and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the Boolean rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs.

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Cited By

Mottet APinsker M(2022)Smooth approximations and CSPs over finitely bounded homogeneous structuresProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533353(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533353
Bodirsky MQuinn-Gregson T(2021)Solving equation systems in ω-categorical algebrasJournal of Mathematical Logic10.1142/S0219061321500203(2150020)Online publication date: 6-Jan-2021
https://doi.org/10.1142/S0219061321500203
Bodirsky MKnäuer SStarke F(2020)ASNP: A Tame Fragment of Existential Second-Order LogicBeyond the Horizon of Computability10.1007/978-3-030-51466-2_13(149-162)Online publication date: 24-Jun-2020
https://doi.org/10.1007/978-3-030-51466-2_13

Index Terms

Temporal Constraint Satisfaction Problems in Fixed-Point Logic
1. Theory of computation

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cover image ACM Conferences

LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

July 2020

986 pages

ISBN:9781450371049

DOI:10.1145/3373718

Conference Chairs:
Holger Hermanns,
Lijun Zhang,
Naoki Kobayashi,
General Chair:
Dale Miller

Copyright © 2020 ACM.

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SIGLOG: ACM Special Interest Group on Logic and Computation
EACSL: European Association for Computer Science Logic
IEEE-CS\DATC: IEEE Computer Society

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Published: 08 July 2020

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LICS '20

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LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science

July 8 - 11, 2020

Saarbrücken, Germany

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LICS '20 Paper Acceptance Rate 69 of 174 submissions, 40%;

Overall Acceptance Rate 215 of 622 submissions, 35%

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Cited By

Mottet APinsker M(2022)Smooth approximations and CSPs over finitely bounded homogeneous structuresProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533353(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533353
Bodirsky MQuinn-Gregson T(2021)Solving equation systems in ω-categorical algebrasJournal of Mathematical Logic10.1142/S0219061321500203(2150020)Online publication date: 6-Jan-2021
https://doi.org/10.1142/S0219061321500203
Bodirsky MKnäuer SStarke F(2020)ASNP: A Tame Fragment of Existential Second-Order LogicBeyond the Horizon of Computability10.1007/978-3-030-51466-2_13(149-162)Online publication date: 24-Jun-2020
https://doi.org/10.1007/978-3-030-51466-2_13

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