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

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

2011-03-17

arxiv.org/abs/1103.3361v1

Computer Science

Formal Languages and Automata Theory

13 pages, submitted

Scientific paper

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.

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