We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 21 October 2009
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.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
