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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.

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