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The residue of vector sets with applications to decidability problems in Petri nets. (English) Zbl 0545.68051
Various right-closed vector sets which are important for analyzing, constructing, or controlling Petri nets are studied. The minimal generating set of a right closed vector set (\(K=K+{\mathbb{N}}^ n)\) is finite and called the residue set of K:\(res(K).\) It is shown that for various sets, which are important for analysis of Petri nets (such as CONTINUAL(\^T), UNBOUNDED, or NOTBLOCKED(\^T)) one can effectively compute their respective residue sets. The new method for calculating the residue set not only solves a number of open problems but also gives a method for controlling a Petri net in order to realize its maximal live subbehaviour. This gives a new solution for the bankers problem described by Dijkstra.

MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68N25 Theory of operating systems
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