A general approach to decomposition of Petri nets.

Abstract

This thesis introduces a general approach to decomposition of Petri nets, i.e., an approach that can be applied to any Petri net. Previous decompositions are applicable only to certain Petri nets, and are associated with the concern that a Petri net may not be decomposable. This thesis removes that concern. Further, a typical previous decomposition does not result in a unique set of components, and needs a decision for choosing a set of components. For example, one decomposition decomposes a Petri net into a set of certain subnets that cover the Petri net, but a Petri net can be covered by more than one possible set of subnets. In contrast, this thesis's approach results in a unique set of components. First, a Petri net is decomposed into sequential components, i.e., components each of which presents a sequence of precedence-ordered events, rather than concurrent events. Two decompositions, which are different in level of detail and in computational complexity, are presented. The simpler of the two can be computed in polynomial time with respect to the Petri net size; the other can be computed in NP-time. A third decomposition adds a recomposability advantage to the first two decompositions. Using the third, any property or problem in a Petri net, such as deadlock, can be completely inspected based on the components. Each decomposition is presented in a graphical form. These decompositions are applicable to verification of a complex system design. Duality is incorporated into the decompositions. In a Petri net dual flow helps trace or monitor the regular token flow. Associated with the above three decompositions are three dual decompositions. Each of the three dual decompositions decomposes a Petri net based on the dual flow. The three dual decompositions simplify the complexity in the dual flow, whereas the first three decompositions simplify the complexity in the regular token flow. In contrast to this thesis, other existing dual decompositions are obtained based on exchanging transitions with places. This thesis adopts a decomposition theory by Naylor, which helps obtain a general decomposition, incorporate one decomposition with another, and incorporate duality.