Low-level dichotomy for Quantified Constraint Satisfaction Problems
Computational Complexity
2011-02-18 v1 Logic in Computer Science
Abstract
Building on a result of Larose and Tesson for constraint satisfaction problems (CSP s), we uncover a dichotomy for the quantified constraint satisfaction problem QCSP(B), where B is a finite structure that is a core. Specifically, such problems are either in ALogtime or are L-hard. This involves demonstrating that if CSP(B) is first-order expressible, and B is a core, then QCSP(B) is in ALogtime. We show that the class of B such that CSP(B) is first-order expressible (indeed, trivially true) is a microcosm for all QCSPs. Specifically, for any B there exists a C such that CSP(C) is trivially true, yet QCSP(B) and QCSP(C) are equivalent under logspace reductions.
Cite
@article{arxiv.1102.3463,
title = {Low-level dichotomy for Quantified Constraint Satisfaction Problems},
author = {Barnaby Martin},
journal= {arXiv preprint arXiv:1102.3463},
year = {2011}
}