Parikh-bounded languages

  • Meera Blattner
  • Michel Latteux
Session 10: M. Nivat, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)


A string y is in C(x), the commutative image of a string x, if y is a permutation of the symbols in x. A language L is Parikh-bounded if L contains a bounded language B and all x in L have a corresponding y in B such that x is in C(y). The central result in this paper is that if L is context-free it is also Parikh-bounded. Parikh's theorem follows as a corollary. If L is not bounded but is a Parikh-bounded language closed under intersection with regular sets, then for any positive integer k there is an x in L such that #(C(x) ∩ L) ≥ k. The notion of Parikh-discreteness is introduced.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Meera Blattner
    • 1
    • 2
  • Michel Latteux
    • 3
  1. 1.University of CaliforniaDavis
  2. 2.Lawrence Livermore National LaboratoryLivermore
  3. 3.Université de LilleVilleneuve d'AscqFrance

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