Low-level dichotomy for quantified constraint satisfaction problems

Martin, Barnaby (2011) Low-level dichotomy for quantified constraint satisfaction problems. Information Processing Letters, 111 (20) . pp. 999-1003. ISSN 0020-0190 [Article] (doi:10.1016/j.ipl.2011.07.010)

Abstract

Building on a result of Larose and Tesson for constraint satisfaction problems (CSPs), 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 trivial) is a microcosm for all QCSPs. Specifically, for any B there exists a C — generally not a core — such that CSP(C) is trivial, yet QCSP(B) and QCSP(C) are equivalent under logspace reductions.

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