Balanced Grammars and Their Languages

  • Authors:
  • Jean Berstel;Luc Boasson

  • Affiliations:
  • -;-

  • Venue:
  • Formal and Natural Computing - Essays Dedicated to Grzegorz Rozenberg [on occasion of his 60th birthday, March 14, 2002]
  • Year:
  • 2002

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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.