Overlapping decompositions and expansions of Petri nets

Overlapping decompositions and expansions are considered to design decentralized controllers for discrete-event systems (DESs) modeled, by Petri nets. The inclusion principle for Petri nets is first defined. It is shown that properties like boundedness, reversibility, and liveness (with a mild additional condition) carry over from the including net to the included net. Moreover, a new property called obstruction, is introduced for the including net, and it is shown that if obstruction does not occur in the including net, then deadlock does not occur in the included net. An expansion procedure, which guarantees inclusion for an overlappingly decomposed Petri net, is then introduced.