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Computer Science > Formal Languages and Automata Theory

arXiv:1103.3361 (cs)
[Submitted on 17 Mar 2011]

Title:On the capabilities of grammars, automata, and transducers controlled by monoids

Authors:Georg Zetzsche
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Abstract:During the last 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.
Comments: 13 pages, submitted
Subjects: Formal Languages and Automata Theory (cs.FL); Group Theory (math.GR)
Cite as: arXiv:1103.3361 [cs.FL]
  (or arXiv:1103.3361v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.1103.3361

Submission history

From: Georg Zetzsche [view email]
[v1] Thu, 17 Mar 2011 09:19:12 UTC (14 KB)
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