- In this paper we model (discrete) reactive systems that may interact with each other by Petri net modules which are classical Petri nets together with a distinguished subset of interface places. We consider then an asynchronous composition operation of modules and, closely related to it, a decomposition operation. We show that any process (concurrent execution) of a composition of two modules can be decomposed into processes of "shifted" components for which a p-composition function exists, and vice versa. Based on this result, a compositional semantics of modules is then defined. The concurrent execution of a module inside a system is called a process sample/fragment of the system w.r.t. that module. We show that, in some circumstances, all the process samples of a system can be generated by e-modules which abstract from some parts of the behaviour by collapsing many consecutive steps into a single one. Some applications of process decomposition to replacement techniques of PetriIn this paper we model (discrete) reactive systems that may interact with each other by Petri net modules which are classical Petri nets together with a distinguished subset of interface places. We consider then an asynchronous composition operation of modules and, closely related to it, a decomposition operation. We show that any process (concurrent execution) of a composition of two modules can be decomposed into processes of "shifted" components for which a p-composition function exists, and vice versa. Based on this result, a compositional semantics of modules is then defined. The concurrent execution of a module inside a system is called a process sample/fragment of the system w.r.t. that module. We show that, in some circumstances, all the process samples of a system can be generated by e-modules which abstract from some parts of the behaviour by collapsing many consecutive steps into a single one. Some applications of process decomposition to replacement techniques of Petri nets, in proving correctness of Petri net structural transformations, and in validation of Petri net models, are further discussed. The last section takes into consideration the model checking problem for Petri net modules. A simulation preoder on Kripke structures with Büchi fairness constraints is considered, which is shown to preserve the delayed version of universal CTL* formulas. Then, the results are transferred to Petri net modules, and discussions on step fairness constraints are provided.…
