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SIAM Journal on Computing
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A structure to decide reachability in Petri nets
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MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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RP'11 Proceedings of the 5th international conference on Reachability problems
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We define 2 operators on relations over natural numbers such that they generalize the operators '+' and '*' and show that the membership and emptiness problem of relations constructed from finite relations with these operators and @? is decidable. This generalizes Presburger arithmetics and allows to decide the reachability problem for those Petri nets where inhibitor arcs occur only in some restricted way. Especially the reachability problem is decidable for Petri nets with only one inhibitor arc, which solves an open problem in [H. Kleine Buning, T. Lettmann, and E. W. Mayr. Projections of vector addition system reachability sets are semilinear. Theoret. Comput. Sci., 64:343-350, 1989]. Furthermore we describe the corresponding automaton having a decidable emptiness problem.