A Kleene Theorem for Polynomial Coalgebras

Authors:
Marcello Bonsangue;Jan Rutten;Alexandra Silva
Affiliations:
LIACS - Leiden University, and Centrum voor Wiskunde en Informatica (CWI),;Centrum voor Wiskunde en Informatica (CWI), and Vrije Universiteit Amsterdam (VUA),;Centrum voor Wiskunde en Informatica (CWI),
Venue:
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Year:
2009

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Abstract

For polynomial functors G , we show how to generalize the classical notion of regular expression to G -coalgebras. We introduce a language of expressions for describing elements of the final G -coalgebra and, analogously to Kleene's theorem, we show the correspondence between expressions and finite G -coalgebras.