Strategies for Minimising the Synthesised ENL-Systems

Elementary Net Systems with Localities (enl-systems) is a class of Petri nets introduced to model gals (globally asynchronous locally synchronous) systems, where some of the components might be considered as logically or physically close and acting synchronously, while others might be considered as loosely connected or residing at distant locations and communicating with the rest of the system in an asynchronous way. The specification of the behaviour of a gals system comes very often in the form of a transition system. The automated synthesis, based on regions, is an approach that allows to construct Petri net models from their transition system specifications. In our previous papers we developed algorithms and tool support for the synthesis of enl-systems from step transition systems, where arcs are labelled by steps (sets) of executed actions. In this paper we focus on the minimisation of the synthesised nets. In particular, we discuss the properties of minimal, companion, and complementary regions, and their role in the process of minimisation of enl-systems. Furthermore, we propose strategies to eliminate redundant regions. Our theoretical results are backed by experiments (the algorithms for the minimisation are implemented within the workcraft framework).