A Soliton Circuit Design System

by

Michael Peter Groves, B.Sc. (Ilons.)

A thesi,s submitted, tor the degree ot Doctor of Philosophy

in the Depørtment of Computer Science Uniuersity of Adelaide

June 1987

-)* \qt-l A, J . ., n -bqr à4 , N ^* CONTENTS

LIST OF TABLES vi LIST OF FIGURES vii

SUMMARY x

DECLARATION xi ACI{NOWLEDGEMENTS xii CIIAPTER 1. INTRODUCTION I

1.1. Soliton circuits 1

1.2. Aims 2

t 1.3. Limitations r)

1.4. Surrmary of the thesis 4

CHAPTER, 2. COMPONENTS 5

2.1. Introduction b

2.2. Connectors 6 2.2.L. Polyacetylene chains 6 2.2.2. Junctions I 2.2.3. Ring junctions 10 2.2.4. Introduction to dynamic circuit diagrams L2

2.3. Soliton switches 13 2.3.L. Logical view 13 2.3.2. The hinge switch 15 2.3.3. A stereochemical switch 16 2.3.4. Conclusions on switch structures t7

2.4. Hills and seesaws 18 2.4.L. Soliton hill 18 2.4.2. Soliton seesaw 19 2.4.3. The carbonyl seesaw 20 2.5. Sids 20 2.5J. Logical view 20 2.5.2. Seesaw sids 2L

2.6. Dynamic circuit diagrams 25 2.6.L. Introduction 25 2.6.2. A symbol for inversion 26 2.6.3. The null symbol 28 2.6.4. N-arm junctions 28 2.6.5. N-arm ring junctions 30 2.6.6. Combinations of symbols 30

(Ð 2.6.7. Summary of symbols 32 2.6.8. Rules for component symbols 34 2.6.9. Rules for dashes in symbols 35 2.6.LO. Tokens 36 2.6.LL. Usefulness of dynamic circuit diagrams 37 2.7. Synthesis and verifrcation of components 39 2.7.1. Introduction 39 2.7.2. Verifi.cation of structures for components 39 2.7.3. External electrical connections 40 2.7.4. Synthesis of a switch 4L 2.7.5. Verification of a switch 43 2.7.6. Synthesis of sids 45 2.7.7. Verifi.cation of sids 46 2.7.8. From switches to soliton circuits 50 2.7.9. Conclusions on the synthesis of components 51 2.8. Conclusions 52

CIIAPTER 3. CIR,CUITS 53 3.1. Introduction 53 3.2. The single soliton switch 54 3.2.L. The problem 54 3.2.2. The structure 55 3.2.3. Logical symbol 58 3.3. Mechanisms and models 60 3.3.1. The mechanism of soliton generation 60 3.3.2. Communication models 62 3.3.3. The soliton model 63 3.3.4: The potential model 64 3.3.5. The amplifier 66 3.3.6. The state model 70

3.4. ,A,mplifiers and inverters 75 3.4.L. Introduction 75 3.4.2. Amplifiers to drive an odd number of inputs tÐ 3.4.3. External inversion 77 3.4.4. Internal inversion 79 3.4.5. Potential inverters 81 3.5. Boolean gates 83 3.5.1. Introduction 83 3.5.2. And gales 84 3.5.3. Or gates 86 3.5.4. External inversion 87 3.5.5. Internal inversion 91 3.5.6. Conclusions on gates formed from arnplifiers and inverters 91 3.5.7. Sub-gates 93 3.5.8. The erclusiue or gate 96

(ii) 3.6. Memories 99 3.6.1. Introduction 99 3.6.2. Selectors 99 3.6.3. A memory cell 101 3.6.4. The fan memory to4 3.6.5. Grid memories 107 3.6.6. The properties of these memories 109 3.7. Circuit design 110 3.7.1. Introduction 110 3.7.2. Design using boolean gates 111 3.7.3. Complex gates LTz 3.7.4. The binary adder as a complex gate 116 3.7.5. Intuitive design 118 3.7 .6. Programmable circuits L20

3.8. Input, output and clocking for soliton circuits L2L 3.8.1. Input and output LzL 3.8.2. Clocking L23 3.9. Conclusions L24

CII.A.PTER 4. MATIIEMATICAL CIRCUIT VER,IFICATION L26 4.1. Introduction L26 4.2. Mathematical state calculations 128 4.2.L. Introduction L28 4.2.2. Legal states L29 4.2.3. Legal states of components and chains L29 4.2.4. Legal states of circuits L32 4.2.5. Examples of state calculations L32 4.2.6. Numbering states 135 4.2.7. Usefulness of mathematical state calculations 138

4.3. State calculation by computer 138 4.3.1. Introduction 138 4.3.2. The algorithm 139 4.3.3. The program L4L 4.3.4. Using the program L4L 4.3.5. Output L43 4.4. Determination of loops L45 4.4.L. Introduction L45 4.4.2. Some assumptions L45 4.4.3. Loops r47 4.4.4. Graphs of circuits L47 4.4.5. Algorithms 148 4.4.6. L