A Petri net based approach to design well behaved discrete event systems

In this paper we introduce a rule-based method, called Φ-synthesis for constructing live, bounded, and reversible (well behaved) systems based on Petri nets. Based on Φ-synthesis method a concurrent system is considered as a pair consisting of the set of processes specified in the system and the set of communication channels describing all interactions that can occur between the processes. A set of synthesis-transformation rules governs the communication channel generating among the elements of the set of the processes. Complex inter-process communication among processes is built up out of synchronisation gates via some specific generated channels based on Φ-rules. Each process possesses an embedded Φ-rule, which controls its communication with the environment. In comparison with the existing synthesis methods, the Φ-synthesis method provides a more general and theoretical basis for future work and application in the field of modelling, automation, and control.