Pushdown automata and multicounter machines, a comparison of computation modes (extended abstract)

Abstract

There are non-context-free languages which are recognizable by randomized pushdown automata even with arbitrarily small error probability. We give an example of a context-free language which cannot be recognized by a randomized pda with error probability smaller than 1/2 - O(log2 n/n) for input size n. Hence nondeterminism can be stronger than probabilism with weakly-unbounded error. Moreover, we construct two deterministic context-free languages whose union cannot be accepted with error probability smaller than 1-3 - 2-Ω(n), where n is the input length. Since the union of any two deterministic context-free languages can be accepted with error probability 1/3, this shows that 1/3 is a sharp threshold and hence randomized pushdown automata do not have amplification. One-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism. © Springer-Verlag Berlin Heidelberg 2003.