Efficient Branch and Bound Search with Application to Computer-Aided Design

150 Pages·1996·2.633 MB·English

by  Xinghao Chen, Michael L. Bushnell (auth.)

EFFICIENT BRANCH AND BOUND
SEARCH WITH APPLICATION
TO COMPUTER-AIDED DESIGN
FRONTIERS IN ELECTRONIC TESTING
Consulting Editor
Vishwani D. Agrawal
Books in the series:
IDDQ Testing of VLSI Circuits,
R. Gulati, C. Hawkins
ISBN: 0-7923-9315-5
Economics of Electronic Design, Manufacture and Test,
M. Abadir, A.P. Ambler
ISBN: 0-7923-9471-2
Testability Concepts for Digital ICs: The Macro Test Approach
F.P.M. Beenker, R.G. Bennetts, A.P. Thijssen
ISBN: 0-7923-9658-8
EFFICIENT BRANCH AND BOUND
SEARCH WITH APPLICATION
TO COMPUTER-AIDED DESIGN
by
Xinghao Chen
Rutgers University
and
Michael L. Bushnell
Rutgers University
~.
"
KLUWER ACADEMIC PUBLISHERS
Boston / Dordrecht / London
Distributors for North America:
Kluwer Academic Publishers
101 Philip Drive
Assinippi Park
Norwell, Massachusetts 02061 USA
Distributors for all other countries:
Kluwer Academic Publishers Group
Distribution Centre
Post Office Box 322
3300 AH Dordrecht, THE NETHERLANDS
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available
from the Library of Congress.
ISBN-13: 978-1-4612-8571-7 e-ISBN-13: 978-1-4613-1329-8
DOl: 10.1007/978-1-4613-1329-8
Copyright © 1996 by Kluwer Academic Publishers
Softcover reprint of the hardcover 1s t edition 1996
All rights reserved. No part of this publication may be reproduced, stored in
a retrieval system or transmitted in any form or by any means, mechanical,
photo-copying, recording, or otherwise, without the prior written permission of
the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park,
Norwell, Massachusetts 02061
Printed on acid-free paper.
To
Christine Yi-Feng Chen
Megan Elizabeth and Amy Katherine Bushnell
CONTENTS
FOREWORD xi
PREFACE xiii
Part I THEORY 1
1 INTRODUCTION 3
1.1 Branch-and-Bound Search 3
1.2 Efficient Branch-and-Bound Search 6
1.3 Justification with Branch-and-Bound 7
1.4 Why Use Justification Equivalence? 7
1.5 Prior Work 8
1.6 Organization of the Book 8
2 JUSTIFICATION EQUIVALENCE 11
2.1 Introduction 11
2.2 Justification Decomposition 13
2.3 Properties 15
2.4 Identification of Shared Justification Decisions 17
2.5 Justification Equivalence 17
2.6 Efficient Representation 19
2.7 An ATPG Example 21
2.8 Summary 23
3 JUSTIFICATION IN FINITE STATE SPACE 25
3.1 Introduction 25
3.2 What is State Justification? 26
viii
3.3 Justifiability of States 28
3.4 State Justification Equivalence 31
3.5 Covering Properties 32
3.6 An Example 33
3.7 Summary 34
Part II APPLICATIONS 35
4 SEQUENTIAL CIRCUIT TEST
GENERATION 37
4.1 Introduction 37
4.2 What is Sequential Circuit Test Generation? 38
4.3 Complexity of Test Generation 41
4.4 How Can Justification Equivalence Help? 42
4.5 Prior Work 44
5 FAULT EFFECTS 55
5.1 Introduction 55
5.2 Fault Effect Analysis 55
5.3 Summary 57
6 THE SEST ALGORITHM 59
6.1 Introduction 59
6.2 The Control Flow 62
6.3 Complexity of Retrieval 64
6.4 Implementation 67
6.5 Summary 73
7 EXPERIMENTAL RESULTS 75
7.1 Introduction 75
7.2 Experimental Procedures 76
7.3 ATPG Time Proportions 76
7.4 SEST Efficiency Evaluation 78
7.5 Benchmark Results 88
7.6 Summary 94
Contents ix
8 REDUNDANCY IDENTIFICATION 97
8.1 Introduction 97
8.2 Why is Redundancy Identification Needed? 98
8.3 Prior Work 98
8.4 Efficient Redundancy Identification 99
8.5 Summary 101
9 LOGIC VERIFICATION 103
9.1 Introduction 103
9.2 Prior Work 105
9.3 Logic Verification via Test Generation 107
9.4 Summary 108
10 CONCLUSION 109
A SEST USER'S GUIDE 111
A.1 INTRODUCTION 111
A.2 COMMAND SYNOPSIS 112
A.3 Options 112
A.4 INPUTS and OUTPUTS 112
A.5 Output Files 117
A.6 Example 117
A.7 Down-Loading SEST from the Disk 122
A.8 Reporting Bugs 123
A.9 Author 123
REFERENCES 125
INDEX 143
FOREWORD
What do languages, alphabets, a printing press, books, a copying machine and a
computer have in common? They all make storage and retrieval of information
possible. History tells us that the rate of progress accelerates with the increase
in the information handling capability. Obviously, we can advance farther if
we can build upon the previous knowledge rather than reinventing everything
from scratch.
According to Robert Tarjan," Actually, computers do much better at speed
chess than at slow chess. If you give both the human and the computer more
time, the human will slaughter the computer. If you speed up things sufficiently
then anybody, even Kasparov, will lose to a computer." (C.W. Gear, Editor,
Computation & Cognition, Philadelphia: SIAM, 1991.) Indeed, using intelli
gence or intuition, a human chess player quickly rejects fruitless moves. The
computer, lacking any intuition, recomputes all details even if the same, or a
similar, situation arises. When we speed up the game, it is the raw speed,
and not the intelligence, of the computer which allows it to win. Suppose we
define intuition as the ability to recognize similarity among things that are
not completely identical. Given that a computer can memorize, can we add
intuition?
There is a class of problems, mostly involving optimization or search, that is
frequently encountered in engineering practice. The complexity of these prob
lems is so great that even fast computers run into difficulty. The authors, Chen
and Bushnell, have conducted significant research on speeding up computer
solutions of this type of problems. Their idea is to save the computed infor
mation for reuse in the future. As the search for a solution progresses, the
amount of information and, hence, the burden of storing it grows. The over
head of information storage and retrieval must be weighed against the cost of
the repeated calculations that could be avoided. The authors determined that
the most useful information is that about sub-spaces containing no solution.
However, the ingenuity of their method lies in procedures through which they
can recognize cases that are only similar to, but are not exactly the same as,
xii
the previously stored cases. The concepts presented in this book are general
and are applicable to a variety of problems.
The book is particularly useful to readers interested in testing of digital cir
cuits. Those who work in that area are familiar with severe limitations of test
generation programs, especially when dealing with sequential circuits. Most
programs make good progress in the beginning, but slow down toward the end
when left with hard-to-detect faults. A reader will find it interesting to exper
iment with the authors' SEST program, supplied with this book. It may run
slightly slower in the beginning due to the time used in storing the learned in
formation. However, as test generation progresses, the program picks up speed
and completes much earlier than most other programs.
The topic of this book is important but has been largely neglected in the liter
ature. I expect that it will be received with the same enthusiasm as the three
previous volumes in the Frontiers in Electronic Testing Series.
Vishwani D. Agrawal
Consulting Editor
Frontiers in Electronic Testing Series
AT&T Bell Laboratories
[email protected]