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A Hierarchy Theorem for Regular Languages over Free Bisemigroups
Zoltán L. Németh1
Acta Cybernetica 16 (2004) 567-577.
Abstract:
In this article a question left open in [1] 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
of languages
accepted by a parenthesizing automaton with
at most 
pairs of parentheses form a strict hierarchy.
In fact, this hierarchy is proper for all alphabets.
Footnotes
Németh 1 Dept. of Computer Science, University of Szeged, P.O.B. 652, 6701 Szeged, Hungary. E-mail: zlnemeth@inf.u-szeged.hu