Cellular Automata and Discrete Complex Systems

Name: Cellular Automata and Discrete Complex Systems | 22nd IFIP WG 1.5 International Workshop, AUTOMATA 2016, Zurich, Switzerland, June 15-17, 2016, Proceedings
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22nd IFIP WG 1.5 International Workshop, AUTOMATA 2016, Zurich, Switzerland, June 15-17, 2016, Proceedings

Matthew Cook Turlough Neary(Editor)

Springer (Publisher)

Published on 1. June 2016

XVI, 199 pages

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978-3-319-39300-1 (ISBN)

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Content

Intro
Preface
Organization
Invited Talk Abstracts
Automata, Semigroups and Dynamical Systems
Propagation, Diffusion and Randomization in Cellular Automata
What Automata Can Provide a Medium for Life?
A Brief Tour of Theoretical Tile Self-Assembly
Contents
Invited Papers
Propagation, Diffusion and Randomization in Cellular Automata
1 Introduction
2 Formal Definitions
2.1 Diamonds and Their Dynamics
2.2 Ergodic Dynamics
3 The Ideal World of 1D Abelian Linear Cellular Automata
3.1 A Characterization of Randomizing CA
3.2 Interesting Reversible Examples
References
What Automata Can Provide a Medium for Life?
1 Introduction
2 Some Historical Notes
3 Methodological Problems
3.1 von Neumann's Fixed-Point Trick
3.2 Computation Universality Is Not Enough
3.3 The Fragility of ``All Mine!''
4 Specific Ergodicity
5 Emergence
6 Life and Evolution
7 Conclusions
References
A Brief Tour of Theoretical Tile Self-Assembly
References
Regular Papers
The Corona Limit of Penrose Tilings Is a Regular Decagon
1 Introduction
2 Corona Limit
3 Penrose Tilings
4 Growth Cellular Automaton on Penrose Tilings
5 Rhombus von Neumann Neighborhood Case
6 The Difference of Growth Speeds
7 Conclusion
References
The Group of Reversible Turing Machines
1 Introduction
1.1 Turing Machines and Their Generalization
1.2 Our Results and Comparisons with Other Groups
1.3 Preliminaries
2 Two Models for Turing Machine Groups
2.1 The Moving Head Model
2.2 The Moving Tape Model
2.3 The Uniform Measure and Reversibility
2.4 Classical Turing Machines
3 Properties of RTM and Interesting Subgroups
3.1 Local Permutations and Oblivious Turing Machines
3.2 Finite-State Automata
3.3 Elementary Turing Machines and the LEF Property of RTM
4 Computability Aspects
4.1 Basic Decidability Results
4.2 The Torsion Problem
References
Exact Discretization of 3-Speed Rational Signal Machines into Cellular Automata
1 Introduction
2 Definitions and Properties
3 Dynamics, Simulation and Normalization
4 Formal Discretization
5 Correctness
6 Conclusion
References
An ``almost dual'' to Gottschalk's Conjecture
1 Introduction
2 Background
3 Post-surjectivity
4 Post-surjectivity on Sofic Groups
5 Conclusions
References
On Finite Monoids of Cellular Automata
1 Introduction
2 Basic Results
3 The Structure of ICA(G
A)
4 Generating Sets of of CA(G
A)
References
Sum of Exit Times in Series of Metastable States in Probabilistic Cellular Automata
1 Introduction
2 The Model
3 Metastable States and Main Results
3.1 Potential Theoretic Approach and Capacities
3.2 Series of Metastable States for PCA Without Self-interaction
4 Sketch of proof of Theorem3.1
4.1 Proof of Lemma3.5
References
Partial Reversibility of One-Dimensional Cellular Automata
1 Introduction
2 Background
2.1 Basics
2.2 Partial Reversibility Classes
3 Reversibility Degree
3.1 Reappraisal of Relative Partial Reversibility in
3.2 Absolute Partial Reversibility
3.3 Partial Reversibility Degree of Individual Elementary Rules
4 Concluding Remarks
References
Two-Dimensional Traffic Rules and the Density Classification Problem
1 Introduction
2 Basics
2.1 Setting
2.2 Presentation of the Problem
2.3 Known Results with Cellular Automata
3 Particle Systems Solutions to the Spacing Problem
3.1 Our Model of IPS
3.2 No Solution to the Strict Spacing Problem
3.3 An IPS that Synchronises Checkerboards
3.4 Glauber Dynamics
4 The Density Classification Problem on Finite Lattices
5 Some Questions
References
Constant Acceleration Theorem for Extended von Neumann Neighbourhoods
1 Definitions
1.1 Cellular Automata
1.2 Picture Recognition
2 Main Result
References
Shrinking and Expanding Cellular Automata
1 Introduction
2 Basics
2.1 Standard CA
2.2 Shrinking and Expanding CA
3 Relating ATM Time to SXCA Time
4 Relating SXCA Time to TM Space
5 Conclusion and Outlook
References
An 8-State Simple Reversible Triangular Cellular Automaton that Exhibits Complex Behavior
1 Introduction
2 Elementary Triangular Partitioned Cellular Automata
3 RETPCA T0347 and Its Properties
3.1 Glider, Block, Fin, and Rotator in T0347
3.2 Changing the Move Direction of a Glider by Blocks
3.3 Glider Guns in T0347
4 T0347 is Computationally Universal
4.1 Showing Turing Universality of Reversible CA
4.2 Making Switch Gate and Inverse Switch Gate Modules in T0347
5 Concluding Remarks
References
Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem
1 Left Group Actions
2 Right Quotient Set Semi-Actions
3 Semi-Cellular and Cellular Automata
4 Invariance, Equivariance, Determination, and Composition of Global Transition Functions
5 Curtis-Hedlund-Lyndon Theorems
6 Invertibility
References
Author Index

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Cellular Automata and Discrete Complex Systems

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