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A Fully Equational Proof of Parikh's Theorem

Published online by Cambridge University Press:  15 December 2002

Luca Aceto ,
Zoltán Ésik  and
Anna Ingólfsdóttir
Luca Aceto
Affiliation:
(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr. Bajersvej 7E, 9220 Aalborg Ø, Denmark; luca@cs.auc.dk.
Zoltán Ésik
Affiliation:
Department of Computer Science, University of Szeged, P.O. Box 652, 6701 Szeged, Hungary.
Anna Ingólfsdóttir
Affiliation:
(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr. Bajersvej 7E, 9220 Aalborg Ø, Denmark; luca@cs.auc.dk.
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Abstract

We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings.

Keywords

Parikh's theoremcommutative context-free languagescommutative rational languagesequational logicvarietiescomplete axiomatizationscommutative idempotent semiringsalgebraically complete commutative idempotent semi rings.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 2: Fixed Points in Computer Science (FICS'01) , April 2002 , pp. 129 - 153
Copyright
© EDP Sciences, 2002

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