Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems)

Bodirsky, Manuel; Mottet, Antoine; Olsak, Miroslav; Oprsal, Jakub; Pinsker, Michael; Willard, Ross

Abstract

The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (innite) nitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the modelcomplete core of the template has a pseudo-Siggers polymorphism, and NPcomplete otherwise. One of the important questions related to this conjecture is whether, similarly to the case of nite structures, the condition of having a pseudo-Siggers polymorphism can be replaced by the condition of having polymorphisms satisfying a xed set of identities of height 1, i.e., identities which do not contain any nesting of functional symbols. We provide a negative answer to this question by constructing for each non-trivial set of height 1 identities a structure whose polymorphisms do not satisfy these identities, but whose CSP is tractable nevertheless. An equivalent formulation of the dichotomy conjecture characterizes tractability of the CSP via the local satisfaction of non-trivial height 1 identities by polymorphisms of the structure. We show that local satisfaction and global satisfaction of non-trivial height 1 identities dier for !-categorical structures with less than double exponential orbit growth, thereby resolving one of the main open problems in the algebraic theory of such structures. 1.

Citation

Bodirsky, M., Mottet, A., Olsak, M., Oprsal, J., Pinsker, M., & Willard, R. (2019, June). Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems). Presented at 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Vancouver, Canada

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• Start Date: Jun 24, 2019
• End Date: Jun 27, 2019
• Acceptance Date: Mar 28, 2019
• Online Publication Date: Aug 5, 2019
• Publication Date: Aug 5, 2019
• Deposit Date: Sep 3, 2019
• Publicly Available Date: Sep 3, 2019
• Publisher: Institute of Electrical and Electronics Engineers
• Book Title: 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• DOI: https://doi.org/10.1109/lics.2019.8785883
• Public URL: https://durham-repository.worktribe.com/output/1142069
• Related Public URLs: https://arxiv.org/abs/1901.04237