8 - Home markings

Summary

A home marking of a system is a marking which is reachable from every reachable marking; in other words, a marking to which the system may always return. The identification of home markings is an interesting issue in system analysis. A concurrent interactive system performs some initial behaviour and then settles in its ultimate cyclic (repetitive) mode of operation. A typical example of such a design is an operating system which, at boot time, carries out a set of initializations and then cyclically waits for, and produces, a variety of input/output operations. The states that belong to the ultimate cyclic behavioural component determine the central function of this type of system. The markings modelling such states are the home markings.

In Section 8.1 we show that live and bounded free-choice systems have home markings. In Section 8.2 we prove a stronger result: the home markings are the reachable markings which mark all the proper traps of the net.

Existence of home markings

Definition 8.1Home marking

Let (N, M₀) be a system. A marking M of the net N is a, home marking of (N, M₀) if it is reachable from every marking of [M₀〉.

We say that (N, M₀) has a home marking if some reachable marking is a home marking.

Using the results of Chapter 3, we can easily prove the following proposition.

Proposition 8.2Home markings of live S- and T-systems

Every reachable marking of a live S-system or a live T-system is a home marking.