Abstract:
Transition systems with independence and asynchronous transition systems are noninterleaving models for concurrency arising from the same simple idea of decorating transitions with events. They differ for the choice of a derived versus a primitive notion of event which induces considerable differences and makes the two models suitable for different purposes. This opens the problem of investigating their mutual relationships, to which this paper gives a fully comprehensive answer.
In details, we characterise the category of extensional asynchronous
transitions systems as the largest full subcategory of the category of
(labelled) asynchronous transition systems which admits 
, the
category of transition systems with independence, as a coreflective
subcategory. In addition, we introduce event-maximal asynchronous
transitions systems and we show that their category is equivalent to
, so providing an exhaustive characterisation of transition
systems with independence in terms of asynchronous transition
systems.
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