Complex sequencing by methods of interpolation in Z/pZ colored Petri nets

The notion of scheduling is a subject that characterizes many contemporary processes. Nevertheless, Petri nets do not present tool satisfying to realize a complex sequencing. The originality of this study is mainly the replacement of the structure of set, associated with colors, by a structure of field Z/pZ allowing to process the succession of colors with mathematics. We introduce an algebraic structure of colors isomorphic with a finite field Z/pZ and a succession law of polynomial type polynomials nets that can be identified to colored Petri net (CPN), except that the arc weights are not predefined, specific or static functions but polynomial functions. This new tool of Petri nets can now be used as basis for ulterior studies on scheduling. We note that this method offers the advantage to operate on complex models, allows dynamic model evolution of PN, and leads to prediction of interesting solutions in scheduling problems and real-time systems.