One-sided Dyck reduction over two letter alphabet and deterministic context-free languages
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
String-rewriting systems
Extended finite automata over groups
Discrete Applied Mathematics
Sequential grammars and automata with valances
Theoretical Computer Science
Formal Languages and Word-Rewriting
Term Rewriting, French Spring School of Theoretical Computer Science, Advanced Course
Computational Calculus and Hardest Languages of Automata with Abstract Storages
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Semigroup automata with rational initial and terminal sets
Theoretical Computer Science
On the capabilities of grammars, automata, and transducers controlled by monoids
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Silent transitions in automata with storage
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is, the bicyclic monoid), they accept a class of languages strictly including the partially blind one-counter languages. Key to the proof is a description of the rational subsets of polycyclic and bicyclic monoids, other consequences of which include the decidability of the rational subset membership problem, and the closure of the class of rational subsets under intersection and complement.