The residue of vector sets with applications to decidability problems in Petri nets (Q797285)

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.