The Chomsky-Schützenberger Theorem for Quantitative Context-Free Languages

  • Manfred Droste
  • Heiko Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7907)


Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schützenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Manfred Droste
    • 1
  • Heiko Vogler
    • 2
  1. 1.Institute of Computer ScienceLeipzig UniversityLeipzigGermany
  2. 2.Department of Computer ScienceTechnische Universität DresdenDresdenGermany

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