Compositional Verification of Liveness Property in Inhibitor-arc Connections of Petri Net Systems

Petri net systems synthesis can construct large systems without the requirement of reachability analysis so that it can reduce the high complexity of analyzing global system. In a synthesis process, such good properties of subsystems as liveness and deadlock-freeness etc, must be preserved in synthesized system. This paper focusses on liveness preservation in inhibitor-arc connection operations. The systems dynamic, concurrent behavior relation i.e. concurrent language relation in inhibitor-arc connections is stressed studied. The corresponding language relation formula is present and proved, and it can be applied to determine liveness of synthesized system in inhibitor-arc connection operations. Furthermore, some criteria are introduced, which are necessary and sufficient for liveness, to determine the liveness of global system by the same ones of local systems. Finally, some examples are given, illustrating the effectiveness of the proposed approach in modeling and analyzing of large systems.