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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1994: STACS 94 pp 109–122Cite as

Space-efficient deterministic simulation of probabilistic automata

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

Abstract

Given a description of a probabilistic automaton (one-head probabilistic finite automaton or probabilistic Turing machine) and an input string x of length n, we ask how much space does a deterministic Turing machine need in order to decide the acceptance of an input string by that automaton?

The question is interesting even in the case of one-head one-way probabilistic finite automata. We call (rational) stochastic languages (S >rat ) the class of languages recognized by these devices with rational transition probabilities and rational cutpoint. Our main results are as follows:

  • The (proper) inclusion of (S >rat ) in Dspace(logn), which is optimal (i.e. (S >rat ) ⪵ Dspace(o(logn))). The previous upper bounds were Dspace(n) [Dieu 1972], [Wang 1992] and Dspace(log n log log n) [Jung 1984].

  • The inclusion of the languages recognized by S(n) ε O(logn) spacebounded probabilistic Turing machines in Dspace(min(2S(n) logn, logn(S(n)+ loglogn))). The previous upper bound was Dspace(logn(S(n)+log logn)) [Jung 1984].

Of independent interest is our technique to compare numbers given in terms of their values modulo a sequence of primes, p 1 < p 2 <⋯ < p n it= O(na) (where a is some constant) in O(log n) deterministic space.

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Authors and Affiliations

  1. Department of Computer Science, University of Rochester, 14627, Rochester, NY

    Ioan I. Macarie

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  1. Ioan I. Macarie
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Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Macarie, I.I. (1994). Space-efficient deterministic simulation of probabilistic automata. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_135

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  • DOI: https://doi.org/10.1007/3-540-57785-8_135

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  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

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