Constraint Satisfaction Problems over Finite Structures

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 poly...

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Veröffentlicht in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 13
Hauptverfasser: Barto, Libor, DeMeo, William, Mottet, Antoine
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 29.06.2021
Schlagworte:
Algebra
Computational complexity
Computer science
Systematics
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Abstract 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 them?We 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.
AbstractList 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 them?We 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.
Author Barto, Libor
Mottet, Antoine
DeMeo, William
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  fullname: DeMeo, William
  organization: Charles University,Faculty of Mathematics and Physics,Department of Algebra,Prague,Czechia
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  givenname: Antoine
  surname: Mottet
  fullname: Mottet, Antoine
  organization: Charles University,Faculty of Mathematics and Physics,Department of Algebra,Prague,Czechia
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Snippet We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both...
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SubjectTerms Algebra
Computational complexity
Computer science
Systematics
Title Constraint Satisfaction Problems over Finite Structures
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