Balanced Grammars and Their Languages

  • Jean Berstel
  • Luc Boasson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2300)


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.


Equivalence Class Derivation Tree Initial Letter Grammar Generate Deterministic Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean Berstel
    • 1
  • Luc Boasson
    • 2
  1. 1.Institut Gaspard Monge (IGM)Université Marne-la-ValléeMarne-la-Vallée Cedex 2
  2. 2.Laboratoire d’informatique algorithmique: fondements et applications (LIAFA)Université Denis-DiderotParis Cedex 05

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