# On the Power of Finite Automata with Both Nondeterministic and Probabilistic States

@article{Condon1998OnTP, title={On the Power of Finite Automata with Both Nondeterministic and Probabilistic States}, author={Anne Condon and Lisa Hellerstein and Samuel Pottle and Avi Wigderson}, journal={SIAM J. Comput.}, year={1998}, volume={27}, pages={739-762} }

We study finite automata with both nondeterministic and random states (npfa's). We restrict our attention to those npfa's that accept their languages with a small probability of error and run in polynomial expected time. Equivalently, we study Arthur--Merlin games where Arthur is limited to polynomial time and constant space.
Dwork and Stockmeyer [SIAM J. Comput., 19 (1990), pp. 1011--1023] asked whether these npfa's accept only the regular languages (this was known if the automaton has only…

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