Semilinearity and Context-Freeness of Languages Accepted by Valence Automata

  • P. Buckheister
  • Georg Zetzsche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the visited edges yields the identity element. By choosing suitable monoids, a variety of automata models can be obtained as special valence automata. This work is concerned with the accepting power of valence automata. Specifically, we ask for which monoids valence automata can accept only context-free languages or only languages with semilinear Parikh image, respectively. First, we present a characterization of those graph products (of monoids) for which valence automata accept only context-free languages. Second, we provide a necessary and sufficient condition for a graph product of copies of the bicyclic monoid and the integers to yield only languages with semilinear Parikh image when used as a storage mechanism in valence automata. Third, we show that all languages accepted by valence automata over torsion groups have a semilinear Parikh image.


Free Product Graph Product Regular Language Storage Mechanism Torsion Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • P. Buckheister
    • 1
  • Georg Zetzsche
    • 1
  1. 1.Fachbereich InformatikTechnische Universität KaiserslauternGermany

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