Comparing Transition Systems with Independence and Asynchronous Transition Systems

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 TSI, 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 TSI, so providing an exhaustive characterisation of transition systems with independence in terms of asynchronous transition systems.