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Minimal realization in bicategories of automata

Published online by Cambridge University Press:  01 April 1998

ROBERT ROSEBRUGH ,
N. SABADINI  and
R. F. C. WALTERS
ROBERT ROSEBRUGH
Affiliation:
Department of Mathematics and Computer Science, Mount Allison University, Sackville, N. B. E0A 3C0 Canada
N. SABADINI
Affiliation:
Dipartimento di Scienze dell'Informazione, Università di Milano, 30135 Milano, Italy
R. F. C. WALTERS
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006 Australia
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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.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 8 , Issue 2 , April 1998 , pp. 93 - 116
Copyright
1998 Cambridge University Press

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Footnotes

This work has been supported by NSERC Canada, Italian MURST and the Australian Research Council.