A Noninterleaving Model of Concurrency Based on Transition Systems with Spatial Structure

In an attempt to devise a general notion of model for spatial logic, we have been led to consider transition systems with an additional so-called spatial structure on the states, with both the transition and the spatial structures described in coalgebraic terms. In this paper we argue that such transition systems with spatial structure can be seen as a noninterleaving model of concurrency, by providing translations to and from a certain category of Petri nets.