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Constraint Satisfaction with Counting Quantifiers 2 by Martin, Barnaby; Stacho, Juraj is a scholarly article available to read on EtoBox.

What is Constraint Satisfaction with Counting Quantifiers 2 about?

We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper, we focus on the complexity of undirected graph templates. As our main contribution, we settle the two principal open questions proposed in (CSR 2012). Firstly, we complete the classification of clique templates by proving a full trichotomy for all possible combinations of counting quantifiers and clique sizes, placing each case either in P, NP-complete or Pspace-complete. This involves resolution of the cases in which we have the single quantifier $\exists^{\geq j}$ on the clique $K_{2j}$. Secondly, we confirm a conjecture from (CSR 2012), which proposes a full dichotomy for $\exists$ and $\exists^{\geq 2}$ on all finite undirected graphs. The main thrust of this second result is the solution of the complexity for the infinite path which we prove is a polynomial-time solvable problem. By adapting the algorithm for the infinite path we are then able to solve the problem for finite paths, and then trees and forests. Thus as a corollary to this wor

Author

Martin, Barnaby; Stacho, Juraj

Published

2013

Language

EN