Collision-Based Computing
(Sprache: Englisch)
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.
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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.
Inhaltsverzeichnis zu „Collision-Based Computing “
1 Symbol Super Colliders1.1 Cellular Automata and Lattice Gases
1.2 Heat, Ice, and Waves
1.3 Colliding-Beams Particle Accelerators
1.4 Why Aristotle Didn't Discover Universal Gravitation
1.5 "On The Nature of the Universe"
1.6 Conclusions
- References
I Twenty Years Ago
2 Design Principles for Achieving High-Performance Submicron Digital Technologies
2.1 Overview
2.1.1 Objectives
2.1.2 Conceptual Framework
2.1.3 Organization
2.2 Principles of Conservative Logic
2.2.1 Motivations
2.2.2 Conservative Logic
2.2.3 Implementation of Conservative Logic in Concrete Computing Devices
2.3 Prospects for Applications to Sub-Micron Digital Technologies
2.3.1 Generalities
2.3.2 Josephson-Effect Switching
2.3.3 Integrated Optics
- References
3 Conservative Logic
3.1 Introduction
3.1.1 Physical Principles Already Contained in the Axioms
3.1.2 Some Physical Principles that Haven't yet Found a Way into the Axioms
3.2 Conservative Logic: The Unit Wire and the Fredkin Gate
3.2.1 Essential Primitives for Computation
3.2.2 Fundamental Constraints of a Physical Nature
3.2.3 The Unit Wire
3.2.4 Conservative-Logic Gates; the Fredkin Gate
3.2.5 Conservative-Logic Circuits
3.3 Computation in Conservative-Logic Circuits; Constants and Garbage
3.4 Computation Universality of Conservative Logic
3.5 Nondissipative Computation
3.6 A "Billiard Ball" Model of Computation
3.6.1 Basic Elements of the Billiard Ball Model
3.6.2 The Interaction Gate
3.6.3 Interconnection; Timing and Crossover; the Mirror
3.6.4 The Switch Gate and the Fredkin Gate
3.7 Garbageless Conservative-Logic Circuits
3.7.1 Terminology: Inverse of a Conservative-Logic Network; Combinational Networks
3.7.2 Role of the Scratchpad Register. Trade-Offs Between Space, Time, and Available Primitives
3.7.3 Circuits that Convert Argument into Result. General-Purpose Conservative-Logic Computers
3.8 Energy Involved in a Computation
3.9 Other Physical Models of Reversible Computation
3.10
... mehr
Conclusions
- References
4 Physics-Like Models of Computation
4.1 Introduction
4.2 Cellular Automata
4.3 Reversible Cellular Automata
4.4 Entropy in RCA
4.5 Conservation Laws in Second-Order RCA
4.6 First-Order RCA
4.7 The Billiard Ball Model
4.8 The BBM Cellular Automaton
4.9 Relationship of BBMCA to Conservative Logic
4.10 Energy in the BBMCA
4.11 Conclusion
4.12 Appendix: A Second-Order, Reversible, Universal Automaton
- References
II The Present and the Future
5 Universal Cellular Automata Based on the Collisions of Soft Spheres
5.1 Fredkin's Billiard Ball Model
5.2 A Soft Sphere Model
5.3 Other Soft Sphere Models
5.4 Momentum Conserving Models
5.4.1 Reflections Without Mirrors
5.4.2 Signal Crossover
5.4.3 Spatially-Efficient Computation
5.4.4 Signal Routing
5.4.5 Dual-Rail Logic
5.4.6 A Fredkin Gate
5.4.7 Implementing the BBMCA
5.4.8 Signal Routing Revisited
5.4.9 A Simpler Extension
5.4.10 Other Lattices
5.5 Relativistic Cellular Automata
5.6 Semi-Classical Models of Dynamics
5.7 Conclusion
- References
6 Computing Inside the Billiard Ball Model
6.1 Definitions
6.1.1 Block Cellular Automata
6.1.2 Reversibility
6.1.3 Simulation
6.1.4 Cellular Automata
6.1.5 Relations with Classical Cellular Automata
6.2 Universality of One-Dimensional Block Cellular Automata
6.3 Billiard Ball Model
6.3.1 Basic Encoding
6.3.2 Conservative Logic
6.3.3 Dual Encoding
6.3.4 Reversible Logic
6.4 Turing Universality of the BBM
6.4.1 Automaton
6.4.2 Counters
6.5 Intrinsic Universality of the BBM
6.5.1 Partitioned Cellular Automata
6.5.2 Intrinsic Universality of the BBM among R-CA
6.5.3 Space-time Simulation
6.5.4 Intrinsic Space-Time Universality of the BBM among CA
6.6 Uncomputable Properties
6.6.1 Reaching a Stable or Periodic Configuration
6.6.2 Reaching a (Sub-)Configuration
- References
7 Universal Computing in Reversible and Number-Conserving Two-Dimensional Cellular Spaces
7.1 Number-Conserving Reversible Cellular Automaton
7.2 Embedding Fredkin Gate in Simple Universal Two-Dimensional Bit-Conserving Reversible Partitioning Cellular Automata
7.2.1 16-State Model with Rotation and Reflection Symmetric Rules
7.2.2 16-State Model with Rotation Symmetric Rules
7.2.3 8-State Triangular Model
7.3 Compact Embedding of Reversible Counter Machine in Universal Number-Conserving Reversible Partitioning Cellular Automata
7.3.1 Reversible Counter Machine
7.3.2 44-State Model
7.3.3 34-State Model
7.4 Conclusion
- References
8 Derivation Schemes in Twin Open Set Logic
8.1 Derived Logical Systems
8.2 Twin Open Set Logic
8.3 Twin Open Set Logic and Classical Logic
8.4 Derivation Schemes in Twin Open Set Logic
8.4.1 Nonstandard Derivation Methods (or what to do when you can't do modus ponens)
8.4.2 Derivation Schemes under Nonstandard Entailment
8.4.3 Nonstandard Implication
8.5 Tautologies in Twin Open Set Logics
8.6 Derivation Schemes in Collision Models
8.7 Conclusion
- References
9 Signals on Cellular Automata
9.1 Some Initial Definitions and Comments
9.1.1 Signals
9.1.2 Signals and Grids
9.2 Transformations of Signals
9.2.1 Transforming Marks on a Cell into Some Right Signal
9.2.2 Some Right Signals from Some Other Ones
9.3 Infinite Families of Signals and Grids
9.3.1 Infinite Families of Signals
9.3.2 Computations and Grids
9.3.3 Infinite Families of Signals (or Waves) on Two-Dimensional Cellular Automaton
9.4 Conclusion
- References
10 Computing with Solitons: A Review and Prospectus
10.1 Computation in Cellular Automata
10.2 Particle Machines (PMs)
10.2.1 Characteristics of PMs
10.2.2 The PM Model
10.2.3 Simple Computation with PMs
10.2.4 Algorithms
10.2.5 Comment on VLSI Implementation
10.2.6 Particles in Other Automata
10.3 Solitons and Computation
10.3.1 Scalar Envelope Solitons
10.3.2 Integrable and Nonintegrable Systems
10.3.3 The Cubic Nonlinear Schrödinger Equation
10.3.4 Oblivious and Transactive Collisions
10.3.5 The Saturable Nonlinear Schrödinger Equation
10.4 Computation in the Manakov System
10.4.1 The Manakov System and its Solutions
10.4.2 State in the Manakov System
10.4.3 Particle Design for Computation
10.5 Conclusion
- References
11 Iterons of Automata
11.1 Homogeneous Nets of Automata
11.2 Cellular Automata Parallel Processing of Strings
11.3 Linear Automaton Media Serial Processing of Strings
11.4 Particles of Cellular Automata
11.5 Filtrons of Serial Processing
11.6 The Automata Based on FCA Window
11.6.1 Jiang Model
11.6.2 AKT Model
11.6.3 FPS Filters
11.6.4 F Model
11.6.5 FM Filters
11.6.6 BRS Models
11.6.7 Soliton Automata
11.7 Automata of Box-Ball Systems and Crystal Systems
11.7.1 Ball Moving Systems
11.7.2 Crystal Systems
11.8 Conclusion
- References
12 Gated Logic with Optical Solitons
12.1 Solitons for Digital Logic
12.1.1 Temporal Soliton Logic Gates
12.1.2 Spatial Soliton Logic Gates
12.1.3 Spatio-Temporal Soliton Logic Gates
12.2 Cascadability of Spatial Soliton Logic Gates
12.2.1 Soliton Logic Gate Transfer Function
12.2.2 Interaction Details
12.2.3 Cascaded Inverters
12.2.4 Cascaded 2-NOR Gates
12.3 Conclusions
- References
13 Finding Gliders in Cellular Automata
13.1 One-Dimensional Cellular Automaton
13.2 Trajectories and Space-Time Patterns
13.3 Basins of Attraction
13.4 Constructing and Portraying Attractor Basins
13.5 Computing Pre-Images
13.5.1 The Cellular Automata Reverse Algorithm
13.5.2 The Z Parameter
13.6 Gliders in One-Dimensional Cellular Automata
13.7 Input-Entropy
13.7.1 Ordered Dynamics
13.7.2 Complex Dynamics
13.7.3 Chaotic Dynamics
13.8 Filtering
13.9 Entropy-Density Signatures
13.10 Automatically Classifying Rule-Space
13.11 Attractor Basin Measures
13.12 Glider Interactions and Basins of Attraction
13.13 Conclusion
13.14 The DDLab Software
- References
14 New Media for Collision-Based Computing
14.1 Molecular Chains
14.2 Molecular Array Processors
14.3 Bulk Media Processors
14.4 Liquid-Crystal Processors
14.5 Granular-Material Processors
14.6 Reaction-Diffusion Processors
14.7 Automata Models of Computing with Localizations
14.7.1 Automata Solitons
14.7.2 Models of Molecular Chains
14.7.3 Models of Molecular Arrays
14.7.4 Automata Worms
14.7.5 Excitable Lattices and Reaction-Diffusion
14.8 Conclusion
- References
15 Lorentz Lattice Gases and Many-Dimensional Turing Machines
15.1 Dynamical Models of Turing Machines
15.2 General Properties of Lorentz Lattice Gases (LLG)
15.3 Description of Models
15.3.1 Regular Lattices
15.3.2 Delaunay Random Lattice
15.4 Some Results on LLG with Fixed Scatterers
15.5 LLG with Flipping Scatterers
15.5.1 Flipping LLG with One Moving Particle
15.5.2 Flipping LLG with Infinitely Many Moving Particles
15.6 Conclusion
- References
16 Arithmetic Operations with Self-Replicating Loops
16.1 Self-Replicating Cellular Automata
16.1.1 Von Neumann's Automaton
16.1.2 Langton's Loop
16.1.3 The New Automaton
16.2 Description of the Automaton
16.2.1 Cellular Space and Initial Configuration
16.2.2 Operation
16.2.3 Example
16.3 Collision-Based Computing: Theoretical Notions
16.3.1 Binary Addition
16.3.2 Binary Multiplication
16.4 Implementation on Self-Replicating Loops
16.4.1 Addition
16.4.2 Multiplication
16.4.3 Combinations of Multiplication and Addition
16.5 Conclusion
- References
17 Implementation of Logical Functions in the Game of Life
17.1 Basic Features of the Game of Life
17.2 Logical Gates
17.3 Collision Reactions
17.3.1 Glider Collisions
17.3.2 Eaters
17.4 Implementation of Logical Gates
17.4.1 Input
17.4.2 Output
17.5 Coupling the Components
17.5.1 The AND-Gate
17.5.2 The OR-Gate
17.5.3 The NOT-Gate
17.6 Implementation of Boolean Equations
17.6.1 Gates Associations
17.6.2 Management of the NOT-Gate
17.7 Binary adder
17.8 Conclusion
- References
18 Turing Universality of the Game of Life
18.1 Some Game of Life Patterns
18.1.1 Adder
18.1.2 Sliding Block Memory
18.1.3 Memory Cell
18.2 Construction of the Turing Machine
18.3 The Finite State Machine
18.3.1 Selection of a Row
18.3.2 Selection of a Column
18.3.3 Set Reset Latch
18.3.4 Collecting Data from the Memory Cell
18.4 The Tape
18.5 Coupling the Finite State Machine with the Stacks
18.6 The Machine in the Pattern
18.7 Extending the Pattern to Make a Universal Turing Machine
18.8 Conclusion
- References
- References
4 Physics-Like Models of Computation
4.1 Introduction
4.2 Cellular Automata
4.3 Reversible Cellular Automata
4.4 Entropy in RCA
4.5 Conservation Laws in Second-Order RCA
4.6 First-Order RCA
4.7 The Billiard Ball Model
4.8 The BBM Cellular Automaton
4.9 Relationship of BBMCA to Conservative Logic
4.10 Energy in the BBMCA
4.11 Conclusion
4.12 Appendix: A Second-Order, Reversible, Universal Automaton
- References
II The Present and the Future
5 Universal Cellular Automata Based on the Collisions of Soft Spheres
5.1 Fredkin's Billiard Ball Model
5.2 A Soft Sphere Model
5.3 Other Soft Sphere Models
5.4 Momentum Conserving Models
5.4.1 Reflections Without Mirrors
5.4.2 Signal Crossover
5.4.3 Spatially-Efficient Computation
5.4.4 Signal Routing
5.4.5 Dual-Rail Logic
5.4.6 A Fredkin Gate
5.4.7 Implementing the BBMCA
5.4.8 Signal Routing Revisited
5.4.9 A Simpler Extension
5.4.10 Other Lattices
5.5 Relativistic Cellular Automata
5.6 Semi-Classical Models of Dynamics
5.7 Conclusion
- References
6 Computing Inside the Billiard Ball Model
6.1 Definitions
6.1.1 Block Cellular Automata
6.1.2 Reversibility
6.1.3 Simulation
6.1.4 Cellular Automata
6.1.5 Relations with Classical Cellular Automata
6.2 Universality of One-Dimensional Block Cellular Automata
6.3 Billiard Ball Model
6.3.1 Basic Encoding
6.3.2 Conservative Logic
6.3.3 Dual Encoding
6.3.4 Reversible Logic
6.4 Turing Universality of the BBM
6.4.1 Automaton
6.4.2 Counters
6.5 Intrinsic Universality of the BBM
6.5.1 Partitioned Cellular Automata
6.5.2 Intrinsic Universality of the BBM among R-CA
6.5.3 Space-time Simulation
6.5.4 Intrinsic Space-Time Universality of the BBM among CA
6.6 Uncomputable Properties
6.6.1 Reaching a Stable or Periodic Configuration
6.6.2 Reaching a (Sub-)Configuration
- References
7 Universal Computing in Reversible and Number-Conserving Two-Dimensional Cellular Spaces
7.1 Number-Conserving Reversible Cellular Automaton
7.2 Embedding Fredkin Gate in Simple Universal Two-Dimensional Bit-Conserving Reversible Partitioning Cellular Automata
7.2.1 16-State Model with Rotation and Reflection Symmetric Rules
7.2.2 16-State Model with Rotation Symmetric Rules
7.2.3 8-State Triangular Model
7.3 Compact Embedding of Reversible Counter Machine in Universal Number-Conserving Reversible Partitioning Cellular Automata
7.3.1 Reversible Counter Machine
7.3.2 44-State Model
7.3.3 34-State Model
7.4 Conclusion
- References
8 Derivation Schemes in Twin Open Set Logic
8.1 Derived Logical Systems
8.2 Twin Open Set Logic
8.3 Twin Open Set Logic and Classical Logic
8.4 Derivation Schemes in Twin Open Set Logic
8.4.1 Nonstandard Derivation Methods (or what to do when you can't do modus ponens)
8.4.2 Derivation Schemes under Nonstandard Entailment
8.4.3 Nonstandard Implication
8.5 Tautologies in Twin Open Set Logics
8.6 Derivation Schemes in Collision Models
8.7 Conclusion
- References
9 Signals on Cellular Automata
9.1 Some Initial Definitions and Comments
9.1.1 Signals
9.1.2 Signals and Grids
9.2 Transformations of Signals
9.2.1 Transforming Marks on a Cell into Some Right Signal
9.2.2 Some Right Signals from Some Other Ones
9.3 Infinite Families of Signals and Grids
9.3.1 Infinite Families of Signals
9.3.2 Computations and Grids
9.3.3 Infinite Families of Signals (or Waves) on Two-Dimensional Cellular Automaton
9.4 Conclusion
- References
10 Computing with Solitons: A Review and Prospectus
10.1 Computation in Cellular Automata
10.2 Particle Machines (PMs)
10.2.1 Characteristics of PMs
10.2.2 The PM Model
10.2.3 Simple Computation with PMs
10.2.4 Algorithms
10.2.5 Comment on VLSI Implementation
10.2.6 Particles in Other Automata
10.3 Solitons and Computation
10.3.1 Scalar Envelope Solitons
10.3.2 Integrable and Nonintegrable Systems
10.3.3 The Cubic Nonlinear Schrödinger Equation
10.3.4 Oblivious and Transactive Collisions
10.3.5 The Saturable Nonlinear Schrödinger Equation
10.4 Computation in the Manakov System
10.4.1 The Manakov System and its Solutions
10.4.2 State in the Manakov System
10.4.3 Particle Design for Computation
10.5 Conclusion
- References
11 Iterons of Automata
11.1 Homogeneous Nets of Automata
11.2 Cellular Automata Parallel Processing of Strings
11.3 Linear Automaton Media Serial Processing of Strings
11.4 Particles of Cellular Automata
11.5 Filtrons of Serial Processing
11.6 The Automata Based on FCA Window
11.6.1 Jiang Model
11.6.2 AKT Model
11.6.3 FPS Filters
11.6.4 F Model
11.6.5 FM Filters
11.6.6 BRS Models
11.6.7 Soliton Automata
11.7 Automata of Box-Ball Systems and Crystal Systems
11.7.1 Ball Moving Systems
11.7.2 Crystal Systems
11.8 Conclusion
- References
12 Gated Logic with Optical Solitons
12.1 Solitons for Digital Logic
12.1.1 Temporal Soliton Logic Gates
12.1.2 Spatial Soliton Logic Gates
12.1.3 Spatio-Temporal Soliton Logic Gates
12.2 Cascadability of Spatial Soliton Logic Gates
12.2.1 Soliton Logic Gate Transfer Function
12.2.2 Interaction Details
12.2.3 Cascaded Inverters
12.2.4 Cascaded 2-NOR Gates
12.3 Conclusions
- References
13 Finding Gliders in Cellular Automata
13.1 One-Dimensional Cellular Automaton
13.2 Trajectories and Space-Time Patterns
13.3 Basins of Attraction
13.4 Constructing and Portraying Attractor Basins
13.5 Computing Pre-Images
13.5.1 The Cellular Automata Reverse Algorithm
13.5.2 The Z Parameter
13.6 Gliders in One-Dimensional Cellular Automata
13.7 Input-Entropy
13.7.1 Ordered Dynamics
13.7.2 Complex Dynamics
13.7.3 Chaotic Dynamics
13.8 Filtering
13.9 Entropy-Density Signatures
13.10 Automatically Classifying Rule-Space
13.11 Attractor Basin Measures
13.12 Glider Interactions and Basins of Attraction
13.13 Conclusion
13.14 The DDLab Software
- References
14 New Media for Collision-Based Computing
14.1 Molecular Chains
14.2 Molecular Array Processors
14.3 Bulk Media Processors
14.4 Liquid-Crystal Processors
14.5 Granular-Material Processors
14.6 Reaction-Diffusion Processors
14.7 Automata Models of Computing with Localizations
14.7.1 Automata Solitons
14.7.2 Models of Molecular Chains
14.7.3 Models of Molecular Arrays
14.7.4 Automata Worms
14.7.5 Excitable Lattices and Reaction-Diffusion
14.8 Conclusion
- References
15 Lorentz Lattice Gases and Many-Dimensional Turing Machines
15.1 Dynamical Models of Turing Machines
15.2 General Properties of Lorentz Lattice Gases (LLG)
15.3 Description of Models
15.3.1 Regular Lattices
15.3.2 Delaunay Random Lattice
15.4 Some Results on LLG with Fixed Scatterers
15.5 LLG with Flipping Scatterers
15.5.1 Flipping LLG with One Moving Particle
15.5.2 Flipping LLG with Infinitely Many Moving Particles
15.6 Conclusion
- References
16 Arithmetic Operations with Self-Replicating Loops
16.1 Self-Replicating Cellular Automata
16.1.1 Von Neumann's Automaton
16.1.2 Langton's Loop
16.1.3 The New Automaton
16.2 Description of the Automaton
16.2.1 Cellular Space and Initial Configuration
16.2.2 Operation
16.2.3 Example
16.3 Collision-Based Computing: Theoretical Notions
16.3.1 Binary Addition
16.3.2 Binary Multiplication
16.4 Implementation on Self-Replicating Loops
16.4.1 Addition
16.4.2 Multiplication
16.4.3 Combinations of Multiplication and Addition
16.5 Conclusion
- References
17 Implementation of Logical Functions in the Game of Life
17.1 Basic Features of the Game of Life
17.2 Logical Gates
17.3 Collision Reactions
17.3.1 Glider Collisions
17.3.2 Eaters
17.4 Implementation of Logical Gates
17.4.1 Input
17.4.2 Output
17.5 Coupling the Components
17.5.1 The AND-Gate
17.5.2 The OR-Gate
17.5.3 The NOT-Gate
17.6 Implementation of Boolean Equations
17.6.1 Gates Associations
17.6.2 Management of the NOT-Gate
17.7 Binary adder
17.8 Conclusion
- References
18 Turing Universality of the Game of Life
18.1 Some Game of Life Patterns
18.1.1 Adder
18.1.2 Sliding Block Memory
18.1.3 Memory Cell
18.2 Construction of the Turing Machine
18.3 The Finite State Machine
18.3.1 Selection of a Row
18.3.2 Selection of a Column
18.3.3 Set Reset Latch
18.3.4 Collecting Data from the Memory Cell
18.4 The Tape
18.5 Coupling the Finite State Machine with the Stacks
18.6 The Machine in the Pattern
18.7 Extending the Pattern to Make a Universal Turing Machine
18.8 Conclusion
- References
... weniger
Bibliographische Angaben
- 2002, XXVIII, 556 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Herausgegeben: Andrew Adamatzky
- Verlag: Springer, Berlin
- ISBN-10: 1852335408
- ISBN-13: 9781852335403
- Erscheinungsdatum: 13.05.2002
Sprache:
Englisch
Rezension zu „Collision-Based Computing “
From the reviews:
Pressezitat
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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