Elementary Transition Systems and Refinement

The model of Elementary Transition Systems has been introduced by the authors as an abstraction of Elementary Net Systems - with a formal embedding in terms of a categorical coreflection, keeping behavioural information like causality, concurrency and conflict, but forgetting the concrete programming of a particular behaviour over an event set using conditions. In this paper we give one example of the advantages of ETS over ENS, - the definition of local state refinement. We show that the well known problems in understanding within nets the simple notion of syntactic substitution of conditions by (sub) nets behaviourally, - these problems seem to disappear when moving to the more abstract level of ETS. Formally, we show that the ETS-version of condition-substitution does satisfy nice and natural properties, e.g., projection and compositionality results w.r.t. a standard notion of transition system morphisms.