Quotient Petri nets*

Abstract

This work introduces the concepts of quotient Petri net (QPN) and dual quotient Petri net (DQPN) as tools to build abstractions of Petri net (PN) structures with three different purposes: a) to have an abstraction (dynamic congruence) of a PN, b) to obtain distributed representations of systems; c) to remove undesired system dynamics. The main advantages are: a) QPN and DQPN preserve sufficient information of the original PN enabling engineers to implement hierarchical or distributed controllers, observers, diagnosers, etc. schemes avoiding/reducing centralized coordinators, b) QPN and DQPN can be efficiently computed by using linear transformations. In fact, a method for computing QPNs and DQPNs is introduced. This work introduces a methodology to compute QPNs and DQPNs that preserve the consistent and conservative from the original PNs.