WITHDRAWN: Modelling and Analysis of Timed and Coloured Petri Nets Using Linear Formal Series in Dioid Algebra

Abstract

This paper presents a set of important results concerning the definition of Coloured Formal Series (CFS). These series are derived from the classical formal power series found in the tropical algebra, used for the temporal description of timed events graphs dynamics. They are differentiated by their coefficient, which is a colour. This new mathematical framework can be used to describe coloured models. We show that it exists a certain class of coloured formal series realised by Timed Coloured Petri Nets (TCPN), i.e., that each TCPN described linearly in the dioid of CFS has a periodic transfer function. For that, we define a restriction of TCPNs yielding the class of Linear TCPN. We present some trivial examples of how use CFS to describe such models.