Extended finite automata over groups
Discrete Applied Mathematics
Group weighted finite transducers
Acta Informatica
Sequential grammars and automata with valances
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Rational subsets of polycyclic monoids and valence automata
Information and Computation
Semigroup automata with rational initial and terminal sets
Theoretical Computer Science
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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.