Minimal realization in bicategories of automata

Authors:
Robert Rosebrugh;N. Sabadini;R. F. C. Walters
Affiliations:
Department of Mathematics and Computer Science, Mount Allison University, Sackville, N. B. E0A 3C0 Canada;Dipartimento di Scienze dell'Informazione, Università di Milano, 30135 Milano, Italy;School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006 Australia
Venue:
Mathematical Structures in Computer Science
Year:
1998

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Abstract

The context of this article is the programme to develop monoidal bicategories with a feedback operation as an algebra of processes, with applications to concurrency theory. The objective here is to study reachability, minimization and minimal realization in these bicategories. In this setting the automata are 1-cells, in contrast with previous studies where they appeared as objects. As a consequence, we are able to study the relation of minimization and minimal realization to serial composition of automata using (co)lax (co)monads. We are led to define suitable behaviour categories and prove minimal realization theorems that extend classical results.