Constraint satisfaction with counting quantifiers

Madelaine, Florent, Martin, Barnaby and Stacho, Juraj (2012) Constraint satisfaction with counting quantifiers. Computer Science - Theory and Applications. In: The 7th International Computer Science Symposium (CSR 2012), 3-7 Jul 2012, Nizhny Novgorod, Russia. ISBN 9783642306419. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-642-30642-6_24)


We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Madelaine F., Martin B., Stacho J. (2012) Constraint Satisfaction with Counting Quantifiers. In: Hirsch E.A., Karhumäki J., Lepistö A., Prilutskii M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg
Research Areas: A. > School of Science and Technology > Computer Science
A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 9656
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Depositing User: Devika Mohan
Date Deposited: 20 Dec 2012 11:21
Last Modified: 24 Apr 2018 14:21

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