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Some observations on 2-way probabilistic finite automata

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 652))

Abstract

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.

This work was supported in part by NSF Grant No. CCR-9111980

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Authors and Affiliations

  1. Department of Computer Science, University of Rhode Island, 02881, Kingston, RI, USA

    B. Ravikumar

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  1. B. Ravikumar
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Rudrapatna Shyamasundar

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© 1992 Springer-Verlag Berlin Heidelberg

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Ravikumar, B. (1992). Some observations on 2-way probabilistic finite automata. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_121

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  • DOI: https://doi.org/10.1007/3-540-56287-7_121

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56287-0

  • Online ISBN: 978-3-540-47507-1

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