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Decidable Hierarchies of Starfree Languages

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

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Abstract

We introduce a strict hierarchy \( \{ \mathbb{L}_n^\mathcal{B} \} \) of language classes which exhausts the class of starfree regular languages. It is shown for all n ≥ 0 that the classes \( \mathbb{L}_n^\mathcal{B} \) have decidable membership problems. As the main result, we prove that our hierarchy is levelwise comparable by inclusion to the dot-depth hierarchy, more precisely, \( \mathbb{L}_n^\mathcal{B} \) contains all languages having dot-depth n +1...2. This yields a lower bound algorithm for the dot-depth of a given language. The same results hold for a hierarchy \( \left\{ {\mathbb{L}_n^\mathcal{L} } \right\}\) and the Straubing-Thérien hierarchy.

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 Gla\er & Heinz Schmitz

Authors
  1. Christian Gla\er
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  2. Heinz Schmitz
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Gla\er, C., Schmitz, H. (2000). Decidable Hierarchies of Starfree Languages. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_41

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  • DOI: https://doi.org/10.1007/3-540-44450-5_41

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