Fair relation and modified synchronic distances in a Petri net (Q1067788)

The notion of synchronic distances in a Petri net may serve as a fundamental basis to achieve synchronization without the use of a central clock in distributed processing systems. However, this notion is so far applicable to restricted subclasses of Petri nets. This paper introduces the concept of a fair relation and presents a modification and extension of synchronic distance measure. The measure can be applied to a wider class of Petri nets. As a result of our modification, it is now possible to say that the synchronic distance between two transitions is finite if and only if they are in a fair relation, i.e. there exists a positive integer k such that neither of them can fire more than k times without firing the other.