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Consistency for counting quantifiers.

Madelaine, Florent and Martin, Barnaby (2018) 'Consistency for counting quantifiers.', in 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). August 27-31, 2018, Liverpool (UK). Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, 11:1-11:13. Leibniz International Proceedings in Informatics (LIPIcs)., 117


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.

Item Type:Book chapter
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Full text:(AM) Accepted Manuscript
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Publisher statement:© B. Martin and F. R. Madelaine; licensed under Creative Commons License CC-BY
Date accepted:13 June 2018
Date deposited:13 July 2018
Date of first online publication:2018
Date first made open access:No date available

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