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Minimal Realization in Bicategories of Automata
 Math. Structures in Computer Science
, 1998
"... The context of this article is the program 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 auto ..."
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The context of this article is the program 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 1cells 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 which extend classical results. This work has been supported by NSERC Canada, Italian MURST and the Australian Research Council 1 Introduction Katis, Sabadini, Walters, and Weld have described bicategories equipped with operations of serial and parallel composition, and feedback modelled as, respectively, composition of 1cells, a tensor product and an operation called...
DOI: 10.1051/ita:2002009 FEEDBACK, TRACE AND FIXEDPOINT SEMANTICS
"... Abstract. We introduce a notion of category with feedbackwithdelay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we ..."
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Abstract. We introduce a notion of category with feedbackwithdelay, closely related to the notion of traced monoidal category, and show that the Circ construction of [15] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal et al. [12] we obtain a description of the free compact
Minimization and Minimal Realization in Span(Graph)
"... The context of this article is the program to study the bicategory of spans of graphs as an algebra of processes, with applications to concurrency theory. The objective here is to study functorial aspects of reachability, minimization and minimal realization. The compositionality of minimization has ..."
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The context of this article is the program to study the bicategory of spans of graphs as an algebra of processes, with applications to concurrency theory. The objective here is to study functorial aspects of reachability, minimization and minimal realization. The compositionality of minimization has application to modelchecking.