New Formal Descriptions for Timed Coloured Petri Nets Using Formal Series

This paper proposes to introduce a dioid of coloured formal series for the description of Timed Coloured Petri Nets (TCPN). These formal series allow us to express TCPN time/event shiftings. As coloured Petri nets can reach a high level of complexity, we first present the coloured formal series for linear systems. Nonetheless, we extend our work to the time and event shiftings in a conflict situation. This example shows the powerful expressiveness of these series and that we can build configurable models for which the transfer function computation can be automated via predictability assumptions.