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Partially-Ordered Two-Way Automata: A New Characterization of DA

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Developments in Language Theory (DLT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2295))

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Abstract

In this paper,we consider finite automata with the restriction that whenever the automaton leaves a state it never returns to it. Equivalently we may assume that the states set is partially ordered and the automaton may never move “backwards” to a smaller state. p] We show that different types of partially-ordered automata characterize different language classes between level 1 and 3/2 of the Straubing-Thérien-Hierarchy. p] In particular, we prove that partially-ordered 2-way DFAs recognize exactly the class UL of unambiguous languages introduced by Schützenberger in 1976. As shown by Schützenberger, this class coincides with the class of those languages whose syntactic monoid is in the variety DA, a specific subclass of all “groupfree” (or “aperiodic”) semigroups.DA has turned out to possess a lot of appealing characterizations. Our result adds one more to these: partially-ordered two-way automata recognize exactly those languages whose syntactic monoid is in DA.

Supported by NSERC of Canada, by FCAR du Québec, and by the Alexander-von-Humboldt-Gesellschaft.Work done while on leave at the Universität Tübingen, Germany.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032, Hans-Meerwein-Straße, Marburg, Germany

    Thomas Schwentick

  2. School of Computer Science, McGill University, 3480 University Street, H3A 2A7, Montréal (Québec), Canada

    Denis Thérien

  3. Theoretische Informatik, UniversitätWürzburg, 97074, Am Hubland, Würzburg, Germany

    Heribert Vollmer

Authors
  1. Thomas Schwentick
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  2. Denis Thérien
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  3. Heribert Vollmer
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Editor information

Editors and Affiliations

  1. Institut für Algebra und Computermathematik Abt. für Theoretische Informatik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Werner Kuich

  2. Department of Computer Science, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkaisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Schwentick, T., Thérien, D., Vollmer, H. (2002). Partially-Ordered Two-Way Automata: A New Characterization of DA. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_20

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  • DOI: https://doi.org/10.1007/3-540-46011-X_20

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  • Print ISBN: 978-3-540-43453-5

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