Towards a simplified building of time Petri Nets reachability graph

An enumerative approach for time Petri nets (or Melin´s model) analysis is presented. In this model, if a transition t is enabled at time τ, it can be fired at any time in the interval [τ+tmax(t)]. It is shown that the firing condition at the nth firing can be expressed by the means of the marking, the enabling point of enabled transitions, and the minimal and maximal elapsed time between to firings. This result leads to an attractive definition of state classes and allows a simple computation of reachable state classes. The approach presented has two main advantages. First, the computation of reachable state classes is more simple and does not require any solution of a system. Second, the graph obtained is a subgraph of that given by M. Menasche (1982)