Probabilistic Length-Reducing Two-Pushdown Automata

Hardness of a separation of nondeterminism, randomization and determinism for polynomial time computations has motivated the analysis of this issue for restricted models of computation. Following this line of research, we consider randomized length-reducing two-pushdown automata (IrTPDA), a natural extension of pushdown automata (PDA). Our main results are as follows. We show that deterministic IrTPDAs are weaker than Las Vegas IrTPDAs which in turn are weaker than Monte Carlo IrTPDAs. Moreover, bounded two-sided error IrTPDAs are stronger than Monte Carlo IrTPDAs and they are able to recognize some languages which cannot be recognized nondeterministically. Finally, we prove that amplification is impossible for Las Vegas and Monte Carlo automata.