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Balanced Grammars and Their Languages

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Formal and Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

Balanced grammars are a generalization of parenthesis grammars in two directions. First, several kind of parentheses are allowed. Next, the set of right-hand sides of productions may be an infinite regular language. XML-grammars are a special kind of balanced grammars. This paper studies balanced grammars and their languages. It is shown that there exists a unique minimal balanced grammar equivalent to a given one. Next, balanced languages are characterized through a property of their syntactic congruence. Finally, we show how this characterization is related to previous work of McNaughton and Knuth on parenthesis languages.

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References

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Author information

Authors and Affiliations

  1. Institut Gaspard Monge (IGM), Université Marne-la-Vallée, 77454, Marne-la-Vallée Cedex 2

    Jean Berstel

  2. Laboratoire d’informatique algorithmique: fondements et applications (LIAFA), Université Denis-Diderot, 75251, Paris Cedex 05

    Luc Boasson

Authors
  1. Jean Berstel
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  2. Luc Boasson
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Berstel, J., Boasson, L. (2002). Balanced Grammars and Their Languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_1

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  • DOI: https://doi.org/10.1007/3-540-45711-9_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

  • eBook Packages: Springer Book Archive

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