Consistency for Counting Quantifiers

Authors Florent R. Madelaine, Barnaby Martin

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Author Details

Florent R. Madelaine
  • LIMOS, Université d'Auvergne, Clermont-Ferrand, France
Barnaby Martin
  • Department of Computer Science, Durham University, U.K.

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Florent R. Madelaine and Barnaby Martin. Consistency for Counting Quantifiers. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We apply the algebraic approach for Constraint Satisfaction Problems (CSPs) with counting quantifiers, developed by Bulatov and Hedayaty, for the first time to obtain classifications for computational complexity. We develop the consistency approach for expanding polymorphisms to deduce that, if H has an expanding majority polymorphism, then the corresponding CSP with counting quantifiers is tractable. We elaborate some applications of our result, in particular deriving a complexity classification for partially reflexive graphs endowed with all unary relations. For each such structure, either the corresponding CSP with counting quantifiers is in P, or it is NP-hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Quantified Constraints
  • Constraint Satisfaction
  • Logic in Computer Science
  • Universal Algebra
  • Computational Complexity


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