Algorithms and tool support for the synthesis of elementary net systems with localities

Abstract

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. While theory of regions is well developed, there is still a shortage of implemented tools capable of dealing with complex real-life system construction. In this research project, we focus on developing algorithms and tool support for the synthesis of ENL-systems from step transition systems (ST-systems), where arcs are labelled by steps (sets) of executed actions. We present an algorithm for deriving non-trivial regions of ST-systems, which is a fundamental algorithm for the synthesis of ENL-systems. We introduce two algorithms for verifying whether a given step transition system can be synthesised to an ENL-system. Also, we present an algorithmic solution to the synthesis problem for ENL/LC-systems - a special subclass of ENL-systems, where conflicts between events are localised. Then, 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 a strategy to eliminate redundant regions. Our theoretical results are backed by experiments. The algorithms are implemented within the WORKCRAFT framework.