Abstract
We investigate relations between transition graphs and net structures. Whereas for a given net structure there always exists a reachability graph, the inverse problem to find a net structure for a given transition graph is not solvable in general. We present sufficient and necessary conditions for several classes of transition graphs such as general, pseudo-bounded, bounded and elementary transition graphs, corresponding to general and (pseudo-)bounded P/T nets or C/E nets. We also give maximal and minimal solutions within an algebraic structure of net structures. The entire investigation is formulated in the framework of multiset theory.
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