Properties of Probabilistic Pushdown Automata

Properties of probabilistic as well as \probabilistic plus nondeterministic" pushdown automata and auxiliary pushdown automata are studied. These models are analogous to their counterparts with nondeterministic and alternating states. Complete characterizations in terms of well-known complexity classes are given for the classes of languages recognized by polynomial time-bounded, logarithmic space-bounded auxiliary pushdown automata with probabilistic states and with \probabilistic plus nondeterministic" states. Also, complexity lower bounds are given for the classes of languages recognized by these automata with unlimited running time. It follows that, by xing an appropriate mode of computation, the di erence between classes of languages such as P and PSPACE, NL and SAC1, PL and Di >(#SAC1) is characterized as the di erence between the number of stack symbols; that is, whether the stack alphabet contains one versus two distinct symbols.