On the Power of Randomized Pushdown Automata

TLDR: The power of randomization for pushdown automata is investigated by investigating the power of decreasing error probabilities, and it is shown that deterministic push down automata are weaker than Las Vegas pushdown Automata, which in turn are stronger than one-sided-error pushdownAutomata.

Abstract: Although randomization is now a standard tool for the design of efficient algorithms or for building simpler systems, we are far from fully understanding the power of randomized computing. Hence it is advisable to study randomization for restricted models of computation.We followthis approach by investigating the power of randomization for pushdown automata.Our main results are as follows. First we show that deterministic pushdown automata are weaker than Las Vegas pushdown automata, which in turn are weaker than one-sided-error pushdown automata. Finally one-sided-error pushdown automata are weaker than (nondeterministic) pushdown automata.In contrast to many other fundamental models of computing there are no known methods of decreasing error probabilities.We show that such methods do not exist by constructing languages which are recognizable by one-sided-error pushdown automata with error probability 1/2, but not by one-sided-error pushdown automata with error probability p < 1/2. On the other hand we construct languages which are not deterministic context-free (resp. not context-free) but are recognizable with arbitrarily small error by one-sided-error (resp. bounded-error) pushdown automata.