Advertisement

The complexity of probabilistic versus deterministic finite automata

  • Andris Ambainis
Session 6b: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)

Abstract

We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains \(\Omega \left( {2^{n\tfrac{{\log \log n}}{{\log n}}} } \right)\) states.

Keywords

Automata theory the complexity of finite automata probabilistic finite automata 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Fr82]
    R. Freivalds, On the growth of the number of states in result of determinization of probabilistic finite automata, Avtomatika i Vicislitelnaja Tehnika, 1982, N.3, 39–42 (in Russian)Google Scholar
  2. [GM79]
    N. Z. Gabbasov, T. A. Murtazina, Improving the estimate of Rabin's reduction theorem, Algorithms and Automata, Kazan University, 1979, 7–10 (in Russian)Google Scholar
  3. [Paz66]
    A. Paz, Some aspects of probabilistic automata, Information and Control, 9(1966)Google Scholar
  4. [Ra63]
    M. O. Rabin, Probabilistic automata, Information and Control, 6(1963), 230–245CrossRefGoogle Scholar
  5. [TB73]
    B. A. Tracktenbrot, Ya. M. Barzdin', Finite Automata: Behaviour and Synthesis. North-Holland, 1973Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Andris Ambainis
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

Personalised recommendations