Marking estimation of Time Petri nets with unobservable transitions

In this paper we present a procedure for the marking estimation of a Time Petri net system in the presence of unobservable (silent) transitions. Starting from the State Class Graph presented by Berthomieu and Diaz, we introduce a new graph called Modified State Class Graph that gives a representation of the evolution of the timed system. Then, we present a procedure that, given a timed observation, i.e., a sequence of observable transitions with their firing time instants, and a time instant τ, allows one to determine in which markings the system can be at time τ by solving a certain number of linear programming problems.