Structures for a homogeneous solution of the state equation of a special timed Petri net and their applications

The transformation rule, such that the Petri net N´ with double-arcs is transformed into the Petri net N with no double-arc, is shown in order to be able to analyze equivalently the Petri net N´ by using the incidence matrix. On this account the authors consider only the Petri net N with no double-arc. The algebraic properties of homogeneous solutions are derived because the general solutions can be found by using homogeneous solutions. The algorithm for obtaining the general solutions of the state equation is proposed. The structures of the subnet with respect to the homogeneous solution are derived