Incremental Abstraction - An Analytical and Algorithmic Perspective on Petri Net Reduction

Bounded Petri nets are in this paper reduced by an incremental abstraction method based on visible bisimulation. An arbitrary bounded Petri net is decomposed into subsystems that are easily transformed to a modular transition system. The basic principle is that places in a Petri net can be interpreted as the synchronous composition of bounded buffers, and a sequence of places can be reduced analytically to a place with extended capacity. Additional restrictions, such as mutual exclusion among shared resources, are formulated as predicates that are easily translated to ordinary transition systems. Since the reduction preserves CTL*-X expressions, it can be used as a stand-alone model checking tool, where temporal properties of the reduced model are easily evaluated. This approach is shown to be very efficient compared to the best known model checking algorithms available in the software tool nuXmv.