Abstract
This paper considers the Petri net reachability problem formulated in terms of nonnegative integer solutions of the state equation and their net representation systems. Our main contributions are twofold. First, we show that algorithms for finding legal transition sequences can be easily given for subclasses of Petri nets where reachability criteria are known or can be formulated by our method. Second, for the general reachability problem where reachability theorems or criteria are not known, and thus an exhaustive search for legal transition sequences is inevitable, we introduce the notion of non-crucial sequences to reduce the search effort.
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