On internal and external characterisations of PT-net building block behaviour

Abstract

Subnets whose relative boundary consists only of transitions, termed building blocks, are used to structure specifications of distributed systems. In this paper we consider the problem how to determine the effects of a building block on its possible environments, considering only its internal structure. External equivalence of building blocks allows one to change these components without affecting the behaviour of the environment and is thus of practical importance. As there are infinitely many potential environments, external equivalence cannot be expressed in a finite form (nor proven) easily. We investigate contexts in which internal equivalence, which is often obtainable without too much effort, is a sufficient condition for external equivalence. The approach chosen here is to specify the building blocks internally by a set of net languages, and to define internal equivalence as the equality of these specifications.

A previous version of this paper appeared under the same title in the Proceedings of the Seventh European Workshop on Application and Theory of Petri Nets, 1986. In the present version an error in the main result has been corrected.