Contexts and embeddings for closed shallow action graphs

摘要: Action calculi, which have a graphical presentation, were introduced to develop theory shared among different calculi for interactive systems. The -calculus, the Petri nets, Ambient calculus and others may all be represented as action calculi. This paper develops part of theory. A recent by two authors was concerned with notion reactive system, essentially category process contexts whose behaviour is presented reduction relation. It shown that one can, any uniformly derive labelled transition system associated behavioural equivalence relations (e.g. trace or bisimilarity) will congruential, under condition certain relative pushouts exist in system. In present we treat closed, shallow (those no free names nested actions) generic application these results. We define graphs embeddings, closely linked forms connection independent interest; it also serves our purpose, enables us demonstrate appropriate exist. Complemented work reported elsewhere, this demonstration yields systems congruences substantial class regard step towards comparable results full class.