On the Capabilities of Grammars, Automata, and Transducers Controlled by Monoids

  • Georg Zetzsche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


During recent decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to exceed the capacity of the original model. Furthermore, we investigate when, in the extended automata model, the nondeterministic variant differs from the deterministic one in capacity. We show that all these conditions are in fact equivalent and present an algebraic characterization. In particular, the open question of whether every language generated by a valence grammar over a finite monoid is context-free is provided with a positive answer.


Linear Extension Regular Language Derivation Tree Left Inverse Valence Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Georg Zetzsche
    • 1
  1. 1.Fachbereich InformatikTechnische Universität KaiserslauternKaiserslauternGermany

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