A hierarchy theorem for regular languages over free bisemigroups

Authors:
Zoltán L. Németh
Affiliations:
Dept. of Computer Science, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary
Venue:
Acta Cybernetica
Year:
2004

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Abstract

In this article a question left open in [2] is answered. In particular, we show that it is essential that in the definition of parenthesizing automata an arbitrary number of parentheses can be used. Moreover, we prove that the classes Regm of languages accepted by a parenthesizing automaton with at most m pairs of parentheses form a strict hierarchy. In fact, this hierarchy is proper for all alphabets.