Earticle

This paper gives a solution of the synchronic distance between any two transitions in a fair Petri net. In order to describe the synchronic distance between two transitions more accurately, the concept of weighted synchronic distance is adopted. The solution method is firstly to add a weighted observe-place between two transitions, and a net system with a weighted observe-place is constructed by assigning a suitable weight function for an arc between a transition and an observe-place. Then the initial tokens of a weighted observe-place are obtained by constructing an augumented coverability tree of a net system with a weighted observe-place. The synchronic distance between two transitions is finally yielded by constructing a coverability tree of a net system with a weighted observe-place, and the corresponding solution algorithms are also given.