Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-18T21:17:45.000Z Has data issue: false hasContentIssue false

Correctness proofs for systolic algorithms: palindromes and sorting

Published online by Cambridge University Press:  03 December 2009

L. Kossen
Affiliation:
Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands
W. P. Weijland
Affiliation:
Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands
Get access

Summary

In designing VLSI-circuits it is very useful, if not necessary, to construct the specific circuit by placing simple components in regular configurations. Systolic systems are circuits built up from arrays of cells and therefore very suitable for formal analysis and induction methods. In two examples correctness proofs are given using bisimulation semantics with asynchronous cooperation. These examples also have been worked out by Hennessy in a setting of failure semantics with synchronous cooperation. Finally the notion of process creation is introduced and used to construct machines with unbounded capacity.

INTRODUCTION

In this article we will present simple descriptions of so-called systolic systems. Such systems can be looked at as a large integration of identical cells in such a way that the behaviour of the total system strongly resembles the behaviour of the individual cells. In fact the total system behaves like one of its individual cells ‘on a larger scale’.

For example one can think of a machine sorting arrays of numbers with a certain maximum length. Suppose we need a machine handling arrays that are much longer. A typical ‘systolic approach’ to this problem would be to try to interconnect the smaller machines such that the total circuit sorts arrays of a greater length. As a matter of fact this specific example will be worked out in the following sections. In designing VLSI-circuits (short for very large scale integrated circuits) it is very useful, if not necessary, to construct the specific circuit by placing simple components in regular configurations. Otherwise one looses all intuition about the behaviour of the circuit that is eventually constructed.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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.

Available formats
×

Save book 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 Dropbox.

Available formats
×

Save book to Google Drive

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.

Available formats
×