Common Special Case: Elementary System Nets

Abstract

Petri nets can be used to describe how the control flow and data flow of a distributed algorithm or system interact. However, one often merely wants to express where a control flow currently stands, whether resources are available, how many messages are pending, etc.

For such an abstract view, it is not necessary to distinguish several kinds of tokens: only “black dots” are used as tokens (such tokens already occurred in the cookie vending machine).

Whenever a transition occurs, “exactly one black token flows through each adjacent arc”. Because this does not have to be instead of explicitly stated, the arcs do not have any labelings. Such system nets are called elementary.

Important aspects of distributed and reactive systems can be modeled appropriately with elementary system nets. We will show this with three examples: an abstract variant of the cookie vending machine, the problem of mutual exclusion, and the crosstalk algorithm.