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Tables of Contents for Colision-Based Computing
Chapter/Section Title
Page #
Page Count
Symbol Super Colliders
1
26
Tommaso Toffoli
Cellular Automata and Lattice Gases
3
7
Heat, Ice, and Waves
10
4
Colliding-Beams Particle Accelerators
14
4
Why Aristotle Didn't Discover Universal Gravitation
18
2
``On The Nature of the Universe''
20
2
Conclusions
22
5
References
22
5
Part I Twenty Years Ago
Design Principles for Achieving High-Performance Submicron Digital Technologies
27
20
Edward F. Fredkin
Tommaso Toffoli
Overview
29
2
Objectives
29
1
Conceptual Framework
30
1
Organization
31
1
Principles of Conservative Logic
31
11
Motivations
31
2
Conservative Logic
33
4
Implementation of Conservative Logic in Concrete Computing Devices
37
5
Prospects for Applications to Sub-Micron Digital Technologies
42
5
Generalities
42
1
Josephson-Effect Switching
42
2
Integrated Optics
44
1
References
45
2
Conservative Logic
47
36
Edward Fredkin
Tommaso Toffoli
Introduction
47
4
Physical Principles Already Contained in the Axioms
48
1
Some Physical Principles that Haven't yet Found a Way into the Axioms
49
2
Conservative Logic: The Unit Wire and the Fredkin Gate
51
5
Essential Primitives for Computation
52
1
Fundamental Constraints of a Physical Nature
52
1
The Unit Wire
53
1
Conservative-Logic Gates; the Fredkin Gate
54
1
Conservative-Logic Circuits
55
1
Computation in Conservative-Logic Circuits; Constants and Garbage
56
3
Computation Universality of Conservative Logic
59
2
Nondissipative Computation
61
3
A ``Billiard Ball'' Model of Computation
64
6
Basic Elements of the Billiard Ball Model
65
1
The Interaction Gate
66
1
Interconnection; Timing and Crossover; the Mirror
67
1
The Switch Gate and the Fredkin Gate
68
2
Garbageless Conservative-Logic Circuits
70
8
Terminology: Inverse of a Conservative-Logic Network; Combinational Networks
71
5
Role of the Scratchpad Register. Trade-Offs Between Space, Time, and Available Primitives
76
1
Circuits that Convert Argument into Result General-Purpose Conservative-Logic Computers
77
1
Energy Involved in a Computation
78
1
Other Physical Models of Reversible Computation
79
1
Conclusions
79
4
References
80
3
Physics-Like Models of Computation
83
24
Norman Margolus
Introduction
83
1
Cellular Automata
83
1
Reversible Cellular Automata
84
1
Entropy in RCA
85
1
Conservation Laws in Second-Order RCA
86
3
First-Order RCA
89
2
The Billiard Ball Model
91
2
The BBM Cellular Automaton
93
4
Relationship of BBMCA to Conservative Logic
97
1
Energy in the BBMCA
98
1
Conclusion
99
1
Appendix: A Second-Order, Reversible, Universal Automaton
99
8
References
103
4
Part II The Present and the Future
Universal Cellular Automata Based on the Collisions of Soft Spheres
107
28
Norman Margolus
Fredkin's Billiard Ball Model
109
2
A Soft Sphere Model
111
3
Other Soft Sphere Models
114
1
Momentum Conserving Models
115
14
Reflections Without Mirrors
116
1
Signal Crossover
116
1
Spatially-Efficient Computation
117
1
Signal Routing
118
1
Dual-Rail Logic
119
1
A Fredkin Gate
120
1
Implementing the BBMCA
121
2
Signal Routing Revisited
123
2
A Simpler Extension
125
3
Other Lattices
128
1
Relativistic Cellular Automata
129
3
Semi-Classical Models of Dynamics
132
1
Conclusion
132
3
References
133
2
Computing Inside the Billiard Ball Model
135
26
Jerome Durand-Lose
Definitions
137
4
Block Cellular Automata
138
1
Reversibility
138
1
Simulation
139
1
Cellular Automata
139
1
Relations with Classical Cellular Automata
140
1
Universality of One-Dimensional Block Cellular Automata
141
2
Billiard Ball Model
143
6
Basic Encoding
144
2
Conservative Logic
146
1
Dual Encoding
147
1
Reversible Logic
148
1
Turing Universality of the BBM
149
3
Automaton
149
1
Counters
150
2
Intrinsic Universality of the BBM
152
5
Partitioned Cellular Automata
153
1
Intrinsic Universality of the BBM among R-CA
154
2
Space-time Simulation
156
1
Intrinsic Space-Time Universality of the BBM among CA
157
1
Uncomputable Properties
157
4
Reaching a Stable or Periodic Configuration
158
1
Reaching a (Sub-)Configuration
158
1
References
159
2
Universal Computing in Reversible and Number-Conserving Two-Dimensional Cellular Spaces
161
40
Kenichi Morita
Yasuyuki Tojima
Katsunobu Imai
Tsuyoshi Ogiro
Number-Conserving Reversible Cellular Automaton
163
2
Embedding Fredkin Gate in Simple Universal Two-Dimensional Bit-Conserving Reversible Partitioning Cellular Automata
165
6
16-State Model with Rotation and Reflection Symmetric Rules
168
2
16-State Model with Rotation Symmetric Rules
170
1
8-State Triangular Model
171
1
Compact Embedding of Reversible Counter Machine in Universal Number-Conserving Reversible Partitioning Cellular Automata
171
23
Reversible Counter Machine
172
5
44-State Model
177
16
34-State Model
193
1
Conclusion
194
7
References
198
3
Derivation Schemes in Twin Open Set Logic
201
30
Michael D. Westmoreland
Joan Krone
Derived Logical Systems
201
2
Twin Open Set Logic
203
6
Twin Open Set Logic and Classical Logic
209
4
Derivation Schemes in Twin Open Set Logic
213
8
Nonstandard Derivation Methods (or what to do when you can't do modus ponens)
215
2
Derivation Schemes under Nonstandard Entailment
217
3
Nonstandard Implication
220
1
Tautologies in Twin Open Set Logics
221
2
Derivation Schemes in Collision Models
223
4
Conclusion
227
4
References
229
2
Signals on Cellular Automata
231
46
Marianne Delorme
Jacques Mazoyer
Some Initial Definitions and Comments
232
11
Signals
233
7
Signals and Grids
240
3
Transformations of Signals
243
13
Transforming Marks on a Cell into Some Right Signal
244
6
Some Right Signals from Some Other Ones
250
6
Infinite Families of Signals and Grids
256
18
Infinite Families of Signals
257
6
Computations and Grids
263
7
Infinite Families of Signals (or Waves) on Two-Dimensional Cellular Automaton
270
4
Conclusion
274
3
References
274
3
Computing with Solitons: A Review and Prospectus
277
22
Mariusz H. Jakubowski
Ken Steiglitz
Richard Squier
Computation in Cellular Automata
278
1
Particle Machines (PMs)
278
8
Characteristics of PMs
279
1
The PM Model
280
1
Simple Computation with PMs
280
1
Algorithms
281
2
Comment on VLSI Implementation
283
1
Particles in Other Automata
283
3
Solitons and Computation
286
2
Scalar Envelope Solitons
286
1
Integrable and Nonintegrable Systems
287
1
The Cubic Nonlinear Schrodinger Equation
287
1
Oblivious and Transactive Collisions
287
1
The Saturable Nonlinear Schrodinger Equation
288
1
Computation in the Manakov System
288
4
The Manakov System and its Solutions
288
1
State in the Manakov System
289
1
Particle Design for Computation
290
2
Conclusion
292
7
References
294
5
Iterons of Automata
299
56
Pawel Siwak
Homogeneous Nets of Automata
303
6
Cellular Automata - Parallel Processing of Strings
309
3
Linear Automaton Media - Serial Processing of Strings
312
5
Particles of Cellular Automata
317
6
Filtrons of Serial Processing
323
3
The Automata Based on FCA Window
326
13
Jiang Model
327
2
AKT Model
329
1
FPS Filters
330
1
F Model
331
2
FM Filters
333
1
BRS Models
333
5
Soliton Automata
338
1
Automata of Box-Ball Systems and Crystal Systems
339
7
Ball Moving Systems
339
3
Crystal Systems
342
4
Conclusion
346
9
References
348
7
Gated Logic with Optical Solitons
355
26
Steve Blair
Kelvin Wagner
Solitons for Digital Logic
358
9
Temporal Soliton Logic Gates
359
2
Spatial Soliton Logic Gates
361
5
Spatio-Temporal Soliton Logic Gates
366
1
Cascadability of Spatial Soliton Logic Gates
367
10
Soliton Logic Gate Transfer Function
367
3
Interaction Details
370
1
Cascaded Inverters
371
3
Cascaded 2-NOR Gates
374
3
Conclusions
377
4
References
379
2
Finding Gliders in Cellular Automata
381
30
Andrew Wuensche
One-Dimensional Cellular Automaton
384
1
Trajectories and Space-Time Patterns
385
1
Basins of Attraction
386
1
Constructing and Portraying Attractor Basins
387
2
Computing Pre-Images
389
3
The Cellular Automata Reverse Algorithm
390
1
The Z Parameter
391
1
Gliders in One-Dimensional Cellular Automata
392
4
Input-Entropy
396
2
Ordered Dynamics
397
1
Complex Dynamics
397
1
Chaotic Dynamics
398
1
Filtering
398
3
Entropy-Density Signatures
401
1
Automatically Classifying Rule-Space
402
3
Attractor Basin Measures
405
2
Glider Interactions and Basins of Attraction
407
1
Conclusion
408
1
The DDLab Software
409
2
References
409
2
New Media for Collision-Based Computing
411
32
Andrew Adamatzky
Molecular Chains
412
2
Molecular Array Processors
414
2
Bulk Media Processors
416
5
Liquid-Crystal Processors
421
1
Granular-Material Processors
422
1
Reaction-Diffusion Processors
423
3
Automata Models of Computing with Localizations
426
12
Automata Solitons
426
1
Models of Molecular Chains
426
6
Models of Molecular Arrays
432
3
Automata Worms
435
1
Excitable Lattices and Reaction-Diffusion
436
2
Conclusion
438
5
References
438
5
Lorentz Lattice Gases and Many-Dimensional Turing Machines
443
26
Leonid A. Bunimovich
Milena A. Khlabystova
Dynamical Models of Turing Machines
445
2
General Properties of Lorentz Lattice Gases (LLG)
447
2
Description of Models
449
1
Regular Lattices
450
1
Delaunay Random Lattice
450
1
Some Results on LLG with Fixed Scatterers
450
2
LLG with Flipping Scatterers
452
12
Flipping LLG with One Moving Particle
453
7
Flipping LLG with Infinitely Many Moving Particles
460
4
Conclusion
464
5
References
465
4
Arithmetic Operations with Self Replicating Loops
469
22
Enrico Petraglio
Gianluca Tempesti
Jean-Marc Henry
Self Replicating Cellular Automata
471
4
Von Neumann's Automaton
471
1
Langton's Loop
472
1
The New Automaton
472
3
Description of the Automaton
475
5
Cellular Space and Initial Configuration
475
1
Operation
476
3
Example
479
1
Collision-Based Computing: Theoretical Notions
480
3
Binary Addition
480
2
Binary Multiplication
482
1
Implementation on Self Replicating Loops
483
4
Addition
484
1
Multiplication
485
1
Combinations of Multiplication and Addition
486
1
Conclusion
487
4
References
490
1
Implementation of Logical Functions in the Game of Life
491
22
Jean-Philippe Rennard
Basic Features of the Game of Life
492
3
Logical Gates
495
1
Collision Reactions
496
2
Glider Collisions
496
2
Eaters
498
1
Implementation of Logical Gates
498
2
Input
499
1
Output
500
1
Coupling the Components
500
5
The AND-Gate
501
1
The OR-Gate
502
2
The NOT-Gate
504
1
Implementation of Boolean Equations
505
3
Gates Associations
505
2
Management of the NOT-Gate
507
1
Binary adder
508
3
Conclusion
511
2
References
511
2
Turing Universality of the Game of Life
513
28
Paul Rendell
Some Game of Life Patterns
514
7
Adder
515
2
Sliding Block Memory
517
1
Memory Cell
518
3
Construction of the Turing Machine
521
1
The Finite State Machine
521
5
Selection of a Row
522
1
Selection of a Column
523
1
Set Reset Latch
523
2
Collecting Data from the Memory Cell
525
1
The Tape
526
8
Coupling the Finite State Machine with the Stacks
534
2
The Machine in the Pattern
536
1
Extending the Pattern to Make a Universal Turing Machine
537
1
Conclusion
537
4
References
538
3
Index
541