On probabilistic pushdown automata

We study the most important probabilistic computation modes for pushdown automata. First we show that deterministic pushdown automata (pda) are weaker than Las Vegas pda, which in turn are weaker than one-sided-error pda. Next one-sidederror pda are shown to be weaker than (nondeterministic) pda. Finally bounded error two-sided error pda and nondeterministic pda are incomparable. To show the limited power of bounded error two-sided pda we apply communication arguments; in particular we introduce a non-standard model of communication which we analyze with the help of the discrepancy method. The power of randomization for pda is considerable, since we construct languages which are not deterministic context-free (resp. not context-free) but are recognizable with even arbitrarily small error by one-sided-error (resp. bounded-error) pda. On the other hand we show that, in contrast to many other fundamental models of computing, error probabilities can in general not be decreased arbitrarily: we construct languages which are recognizable by one-sided-error pda with error probability 12 , but not by one-sided-error pushdown automata with error probability p < 12 . A similar result, with error probability 1 3 , holds for bounded error two-sided error pda.