Universal models in categories for process synchronization
In the first part of the paper we show how to construct categorical models for Milner's CCS [Mil80], Hoare's CSP [Hoa78], and similarly defined calculi for synchronized and parallel computations.
We consider a generic category C of processes with morphisms which are labelled by strings of actions belonging to a monoid A. We define the synchronization between two processes in C as a functor (if it exists) from a subcategory of C × C into C. We introduce the notions of categorical semantics and good categorical semantics for processes.
In the second part of the paper we show that the Categories of Trees we will define, is optimal for most synchronizations described in the literature. That result is presented also in the framework of the Enriched Category Theory [Law74] for indicating its meaning in terms of an internal logic [Law74].
KeywordsBoolean Algebra Universal Model Atomic Action Label Tree Internal Logic
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