Abstract
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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Zetzsche, G. (2011). On the Capabilities of Grammars, Automata, and Transducers Controlled by Monoids. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_17
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DOI: https://doi.org/10.1007/978-3-642-22012-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22011-1
Online ISBN: 978-3-642-22012-8
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