Submarking reachability of marked graphs

Reachability of marked graphs is generalized to that with respect to any subgraph of the marked graph. It is shown that the existence of a minimum firing count vector satisfying a set of equality and inequality constraints is equivalent to the submarking reachability. A necessary and sufficient condition is presented for the existence of the minimum firing count vector together with its constructing algorithm. The result can be applied to the problem of finding the shortest firing sequence which arises in practical sequential control problems.