Two applications of complementation via inductive counting

A recent proof that nondeterministic space-bounded complexity classes are closed under complementation is used to develop two further applications of the inductive counting technique. An errorless probabilistic algorithm is given for the undirected graph s-t connectivity problem that runs in O(log n) space and polynomial expected time, and it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fan-in circuits (or, equivalently, nondeterministic auxiliary pushdown automata or tree-sized bounded alternating Turing machines). As one consequence, small numbers of role switches in two-person pebbling can be eliminated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>