Collision-Based Computing - Andrew Adamatzky

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Collision-Based Computing

By: Andrew Adamatzky (Editor)

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Paperback | 13 May 2002

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580 Pages

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22.86 x 15.24 x 3.18

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Collision-Based Computing presents a unique overview of computation with mobile self-localized patterns in non-linear media, including computation in optical media, mathematical models of massively parallel computers, and molecular systems.
It covers such diverse subjects as conservative computation in billiard ball models and its cellular-automaton analogues, implementation of computing devices in lattice gases, Conway's Game of Life and discrete excitable media, theory of particle machines, computation with solitons, logic of ballistic computing, phenomenology of computation, and self-replicating universal computers.
Collision-Based Computing will be of interest to researchers working on relevant topics in Computing Science, Mathematical Physics and Engineering. It will also be useful background reading for postgraduate courses such as Optical Computing, Nature-Inspired Computing, Artificial Intelligence, Smart Engineering Systems, Complex and Adaptive Systems, Parallel Computation, Applied Mathematics and Computational Physics.

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From the reviews:

"This book contains a collection of articles on the theme of how to do computation with mobile objects or patterns in nonlinear media, as exemplified most vividly by collision-based computing. ... Each chapter in the book has its own list of references ... . This book is recommended for anyone looking for an introduction to the fascinating developing subject of collision-based computing on a non-trivial level." (Menachem Dishon, Mathematical Reviews, Issue 2007 b)

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Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Mathematical Theory of Computation Science Physics Nuclear Physics Computer Programming & Software Development Human-Computer Interaction User Interface Design & Usability Mathematical Physics

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

Collision-Based Computing

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

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