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# Constraint Satisfaction Problems over Finite Structures

Publikationstyp

Conference Paper

Publikationsdatum

2021-06-29

Sprache

English

Volume

2021-June

Article Number

9470670

Citation

36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2021)

Contribution to Conference

Publisher DOI

Scopus ID

We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a natural algebraic question: which finite algebras admit only polynomially many homomorphisms into themWe give some sufficient and some necessary conditions for a finite algebra to have this property. In particular, we show that every finite equationally nontrivial algebra has this property which gives us, as a simple consequence, a complete complexity classification of CSPs over two-element structures, thus extending the classification for two-element relational structures by Schaefer (STOC'78).We also present examples of two-element structures that have bounded width but do not have relational width (2,3), thus demonstrating that, from a descriptive complexity perspective, allowing operations leads to a richer theory.