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On the Power of Las Vegas II. Two-Way Finite Automata

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Automata, Languages and Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

The investigation of the computational power of randomized computations is one of the central tasks of complexity and algorithm theory. This paper continues in the comparison of the computational power of Las Vegas computations with the computational power of deterministic and nondeterministic ones. While for one-way finite automata the power of different computational modes was successfully determined one does not have any nontrivial result relating the power of determinism, Las Vegas and nondeterminism for two-way finite automata. The three main results of this paper are the following ones.

  1. (i)

    If, for a regular language L, there exist small two-way nondeterministic finite automata for both L and L C, then there exists a small two-way Las Vegas finite automaton for L.

  2. (ii)

    There is a quadratic gap between nondeterminism and Las Vegas for two-way finite automata.

  3. (iii)

    For every k ∈ ℕ, there is a regular language Sk such that Sk can be accepted by two-way Las Vegas finite automaton with O(k) states, but every two-way deterministic finite automaton recognizing Sk has at least Ω(k2/log2k) states.

The work on this paper has been supported by DFG-Project HR 14/3-2.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik I, RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Juraj Hromkovič

  2. Fachbereich Informatik, Johann Wolfgang Goethe Universität Frankfurt, Robert Mayer Straße 11-15, 60054, Frankfurt am Main, Germany

    Georg Schnitger

Authors
  1. Juraj Hromkovič
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  2. Georg Schnitger
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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Hromkovič, J., Schnitger, G. (1999). On the Power of Las Vegas II. Two-Way Finite Automata. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_40

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  • DOI: https://doi.org/10.1007/3-540-48523-6_40

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  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

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