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A Logical Characterization of Systolic Languages

  • Logic II
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

In this paper we study, in the framework of mathematical logic, ℒ(SBTA) i.e. the class of languages accepted by Systolic Binary Tree Automata. We set a correspondence (in the style of Büchi Theorem for regular languages) between ℒ(SBTA) and MSO[Sig], i.e. a decidable Monadic Second Order logic over a suitable infinite signature Sig. We also introduce a natural subclass of ℒ(SBTA) which still properly contains the class of regular languages and which is proved to be characterized by Monadic Second Order logic over a finite signature Sig′ ⊂ Sig. Finally, in the style of McNaughton Theorem for star free regular languages, we introduce an expression language which precisely denotes the class of languages defined by the first order fragment of MSO[Sig′].

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Author information

Authors and Affiliations

  1. Dipartimento Scienze dell'Informazione, Università di Roma(La Sapienza), Via Salaria 113, 00198, Italy

    Angelo Monti

  2. Dipartimento di Matematica e Informatica, Università di Udine, Via Delle Scienze 206, 33100, Italy

    Adriano Peron

Authors
  1. Angelo Monti
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  2. Adriano Peron
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Monti, A., Peron, A. (1998). A Logical Characterization of Systolic Languages. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028582

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  • DOI: https://doi.org/10.1007/BFb0028582

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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