A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata

@article{Dwork1990ATC,
title={A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata},
author={Cynthia Dwork and Larry J. Stockmeyer},
journal={SIAM J. Comput.},
year={1990},
volume={19},
pages={1011-1023}
}

It is shown that if a 2-way probabilistic nite state automaton (2pfa) M recognizes a nonregular language L with error probability bounded below 1/2, then there is a positive constant b (depending on M) such that, for innnitely many inputs x, the expected running time of M on input x must exceed 2 n b where n is the length of x. This complements a result of Freivalds showing that 2pfa's can recognize certain nonregular languages in exponential expected time. It also establishes a time complexityâ€¦Â CONTINUE READING