A Kleene Theorem for Forest Languages

  • Lutz Straßburger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)


This paper proposes an alternative approach to the standard notion of rational (or regular) expression for tree languages. The main difference is that in the new notion we have only one concatenation operation and only one star-operation, instead of many different ones. This is achieved by considering forests instead of trees over a ranked alphabet, or, algebraicly speaking, by considering cartesian categories instead of term-algebras. The main result is that in the free cartesian category the rational languages and the recognizable languages coincide. For the construction of the rational expression for a recognizable language it is not necessary to extend the alphabet. We only use operations that can be defined with the algebraic structure provided by cartesian categories.


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Lutz Straßburger
    • 1
  1. 1.INRIA Saclay, Île-de-France, Équipe-projet Parsifal École Polytechnique, LIXPalaiseau CedexFrance

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