The Boolean Closure of Growing Context-Sensitive Languages
Fundamenta Informaticae
Growing Grammars and Length-reducing Automata
Fundamenta Informaticae - Non-Classical Models of Automata and Applications II
The Boolean Closure of Growing Context-Sensitive Languages
Fundamenta Informaticae
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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 ( $\mathsf{lrTPDA}$), a natural extension of pushdown automata ( $\mathsf{PDA}$). Our main results are as follows. We show that deterministic $\mathsf{lrTPDA}$s are weaker than Las Vegas $\mathsf{lrTPDA}$s which in turn are weaker than Monte Carlo $\mathsf{lrTPDA}$s. Moreover, bounded two-sided error $\mathsf{lrTPDA}$s are stronger than Monte Carlo $\mathsf{lrTPDA}$s 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.