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Nondeterminism versus Determinism for Two-Way Finite Automata: Generalizations of Sipser’s Separation

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

Whether there exists an exponential gap between the size of a minimal deterministic two-way automaton and the size of a minimal nondeterministic two-way automaton for a specific regular language is a long standing open problem and surely one of the most challenging problems in automata theory. Twenty four years ago, Sipser [M. Sipser: Lower bounds on the size of sweeping automata. ACM STOC ’79, 360–364] showed an exponential gap between nondeterminism and determinism for the so-called sweeping automata which are automata whose head can reverse direction only at the endmarkers. Sweeping automata can be viewed as a special case of oblivious two-way automata with a number of reversals bounded by a constant.

Our first result extends the result of Sipser to general oblivious two-way automata with an unbounded number of reversals. Using this extension we show our second result, namely an exponential gap between determinism and nondeterminism for two-way automata with the degree of non-obliviousness bounded by o(n) for inputs of length n. The degree of non-obliviousness of a two-way automaton is the number of distinct orders in which the tape cells are visited.

Supported by DFG grants HR 1416-1 and SCHN 50312-1.

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Author information

Authors and Affiliations

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

    Juraj Hromkovič

  2. Fachbereich Informatik, Johann-Wolfgang-Goethe Universität, 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. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Hromkovič, J., Schnitger, G. (2003). Nondeterminism versus Determinism for Two-Way Finite Automata: Generalizations of Sipser’s Separation. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_36

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  • DOI: https://doi.org/10.1007/3-540-45061-0_36

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  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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