Space-efficient deterministic simulation of probabilistic automata

Extended abstract
  • Ioan I. Macarie
Conference paper
Part of the Lecture Notes in Computer Science book series (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 (Srat>) 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 (Srat>) in Dspace(logn), which is optimal (i.e. (Srat>) ⪵ 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, p1 < p2 <⋯ < pn it= O(na) (where a is some constant) in O(log n) deterministic space.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Ioan I. Macarie
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester

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