eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
11:1
11:13
10.4230/LIPIcs.MFCS.2018.11
article
Consistency for Counting Quantifiers
Madelaine, Florent R.
1
Martin, Barnaby
2
LIMOS, Université d'Auvergne, Clermont-Ferrand, France
Department of Computer Science, Durham University, U.K.
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.11/LIPIcs.MFCS.2018.11.pdf
Quantified Constraints
Constraint Satisfaction
Logic in Computer Science
Universal Algebra
Computational Complexity