Abstract
The problem to find the initial markings which enable the specified firing counts of transitions ina Petri net is of particular importance in both practical and theoretical points of view. In practice, it corresponds to find initial resources necessary for realizing given occurrences of events. In theory, it constitutes alternative approach to the reachability problem when the specified firing counts are the nonnegative integer solution of the matrix equation of the reachability problems.
The notion of the Token Flow Graph (TFG) is introduced in this paper to analyze and solve the problem. TFG is obtained by expanding the original Petri net according to the firing count of each transition. It indicates the paths of possible token flow when the specified firing counts are realized. TFG and its extended form give the sufficient condition to bo satisfied by the initial markings which enable the specified firing counts, and, consequently, provide the way to find the enabling initial markings and the partial order of transition firings as well.
