Some Observations on 2-way Probabilistic Finite Automata

R. Freivalds [Fr81] initiated a study of 2-way probabilistic finite automata (2-pfa's) with bounded error by proving the surprising result that such an automaton can recognize the nonregular language {On1n¦n ≥ 1}. A number of interesting results have hence been obtained about 2-pfa's, notably by Greenberg and Weiss [Gr86], Dwork and Stockmeyer [Dw89], [Dw90] and Condon and Lipton [Co89]. In this work, we present new results about the class 2-PFA, the class of languages accepted by 2-pfa's including the following: (i) 2-PFA includes all the bounded semilinear languages, and (ii) 2-PFA includes all languages accepted by deterministic blind counter machines. We also show that a pebble enhances the power of a 2-pfa with unbounded error probability. We study the closure properties of the class 2-PFA and in that context, identify a (possibly) nontrivial subclass of 2-PFA. We conclude with some open problems and directions for further work.

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