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Languages of Dot-Depth 3/2

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

We prove an effective characterization of languages having dot-depth 3/2. Let B 3/2 denote this class, i.e., languages that can be written as finite unions of languages of the form u 0 L 1 u 1 L 2 u 2 ...L n u n, where u i ∈ A* and L i are languages of dot-depth one. Let F be a deterministic finite automaton accepting some language L. Resulting from a detailed study of the structure of B 3/2, we identify a pattern P (cf. Fig. 2) such that L belongs to B 3/2 if and only if F does not have pattern P in its transition graph. This yields an NL-algorithm for the membership problem for B 3/2.

Due to known relations between the dot-depth hierarchy and symbolic logic, the decidability of the class of languages definable by Σ 2-formulas of the logic FO[<, min, max, S, P] follows. We give an algebraic interpretation of our result.

Supported by the Studienstiftung des Deutschen Volkes.

Supported by the Deutsche Forschungsgemeinschaft (DFG), grant Wa 847/4-1.

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Würzburg, 97074, Würzburg, Germany

    Christian Glaßer & Heinz Schmitz

Authors
  1. Christian Glaßer
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  2. Heinz Schmitz
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Glaßer, C., Schmitz, H. (2000). Languages of Dot-Depth 3/2. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_46

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  • DOI: https://doi.org/10.1007/3-540-46541-3_46

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  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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