  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.
