Polycyclic and Bicyclic Valence Automata

Authors:
Elaine Render;Mark Kambites
Affiliations:
School of Mathematics, University of Manchester, Manchester, England M13 9PL;School of Mathematics, University of Manchester, Manchester, England M13 9PL
Venue:
Language and Automata Theory and Applications
Year:
2008

Citing 3
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Abstract

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 proofs 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 for these monoids, and the closure of the class of rational subsets under intersection and complement.