On the Synthesis of General Petri Nets
Résumé
A polynomial algorithm was given by the authors and Bernardinello for synthesizing pure weighted Petri nets from finite labeled transition systems. The limitation to pure nets, serious in practice e.g. for modelling waiting loops in communication protocols, may be removed by a minor adaptation of the algorithm, working for general Petri nets fired sequentially. The rule of sequential firing reduces also the expressivity of Petri nets, since it forces a concurrent interpretation on every diamond. This limitation may also be removed by leaving sequential transition systems and lifting the algorithm to step transition systems, which amounts to extract the effective contents of the coreflection between Petri step transition sytems and general Petri nets established by Mukund. By the way, the categorical correspondences between transition systems or step transition systems and nets are re-examined and simplified to Galois connections in the usual setting of ordered sets.