An extension theorem with an application to formal tree series

Authors:
Stephen L. Bloom;Zoltán Ésik
Affiliations:
Department of Computer Science, Stevens Institute of Technology, Hoboken, NJ;Institute for Informatics, University of Szeged, Szeged, Hungary
Venue:
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Year:
2003

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Abstract

Suppose that T is a grove theory, and M is a Conway or iteration matrix theory which is a subtheory of T. We provide a sufficient condition under which the dagger operation on M can be extended to T so that T becomes a Conway or iteration theory. Moreover, we prove a general Kleene type theorem applicable to all grove theories which are Conway theories. We discuss applications to synchronization trees and formal tree series.