The Evolutionary Design of Collective Computation in Cellular Automata

We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which "particles" embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how machine-learning processes can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation. Subitted to Machine Learning Journal.

[1]  M Mitchell,et al.  The evolution of emergent computation. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Alvy Ray Smith,et al.  Real-Time Language Recognition by One-Dimensional Cellular Automata , 1972, J. Comput. Syst. Sci..

[3]  Tad Hogg,et al.  Spawn: A Distributed Computational Economy , 1992, IEEE Trans. Software Eng..

[4]  Kenneth Steiglitz,et al.  When Can Solitons Compute? , 1996, Complex Syst..

[5]  Michael P. Wellman.  A Market-Oriented Programming Environment and its Application to Distributed Multicommodity Flow Problems , 1993, J. Artif. Intell. Res..

[6]  Jacques Mazoyer,et al.  An Overview of the Firing Squad Synchronization Problem , 1986, Automata Networks.

[7]  Russell Beale,et al.  Handbook of Neural Computation , 1996 .

[8]  J. Crutchfield.  The calculi of emergence: computation, dynamics and induction , 1994 .

[9]  Alan S. Perelson,et al.  The immune system, adaptation, and machine learning , 1986 .

[10]  Kenneth Steiglitz,et al.  Programmable Parallel Arithmetic in Cellular Automata Using a Particle Model , 1994, Complex Syst..

[11]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[12]  Peter Gacs.  Nonergodic one-dimensional media and reliable computation , 1985 .

[13]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[14]  Yves Robert,et al.  Automata networks in computer science : theory and applications , 1987 .

[15]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[16]  J. Crutchfield,et al.  The attractor—basin portrait of a cellular automaton , 1992 .

[17]  Stephanie Forrest,et al.  Computer immunology , 1997, CACM.

[18]  Annalisa Massini,et al.  Fast Parallel Arithmetic on Cellular Automata , 1994, Complex Syst..

[19]  H. F. Chau,et al.  CLASSIFYING RATIONAL DENSITIES USING TWO ONE-DIMENSIONAL CELLULAR AUTOMATA , 1998 .

[20]  Tommaso Toffoli,et al.  Cellular automata machines - a new environment for modeling , 1987, MIT Press series in scientific computation.

[21]  L. Darrell Whitley,et al.  The evolution of emergent computation in cellular automata , 1998 .

[22]  J. Crutchfield,et al.  Turbulent pattern bases for cellular automata , 1993 .

[23]  Geoffrey E. Hinton,et al.  A general framework for parallel distributed processing , 1986 .

[24]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..

[25]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine-mediated learning.

[26]  Franco Bagnoli,et al.  Cellular Automata , 2002, Lecture Notes in Computer Science.

[27]  James P. Crutchfield,et al.  Evolving Globally Synchronized Cellular Automata , 1995, ICGA.

[28]  E. F. Codd,et al.  Cellular automata , 1968 .

[29]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[30]  Capcarrere,et al.  Two-state, r=1 Cellular Automaton that Classifies Density. , 1996, Physical review letters.

[31]  S. Wolfram.  Statistical mechanics of cellular automata , 1983 .

[32]  Moshe Sipper,et al.  Co-evolving architectures for cellular machines , 1997 .

[33]  Joel M. Crichlow.  An introduction to distributed and parallel computing , 1988 .

[34]  James P. Crutchfield,et al.  Statistical Dynamics of the Royal Road Genetic Algorithm , 1999, Theor. Comput. Sci..

[35]  Moshe Sipper,et al.  Evolution of Parallel Cellular Machines: The Cellular Programming Approach , 1997 .

[36]  Jordan B. Pollack,et al.  Coevolutionary Learning: A Case Study , 1998, ICML.

[37]  Terrence J. Sejnowski,et al.  The Computational Brain , 1996, Artif. Intell..

[38]  James P. Crutchfield.  Spatio-temporal complexity in nonlinear image processing , 1988 .

[39]  Bhavin Sheth,et al.  Binary Addition on Cellular Automata , 1991, Complex Syst..

[40]  Gary D. Doolen.  Lattice Gas Methods For Partial Differential Equations , 1990 .

[41]  Melanie Mitchell,et al.  Evolving cellular automata to perform computations: mechanisms and impediments , 1994 .

[42]  Jean-Louis Deneubourg,et al.  The dynamics of collective sorting robot-like ants and ant-like robots , 1991 .

[43]  Danny Dolev,et al.  Authenticated Algorithms for Byzantine Agreement , 1983, SIAM J. Comput..

[44]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[45]  E. F. Moore.  The firing squad synchronization problem , 1964 .

[46]  Tommaso Toffoli,et al.  Cellular automata : proceedings of an interdisciplinary workshop, Los Alamos, New Mexico 87545, USA, March 7-11, 1983 , 1984 .

[47]  James P. Crutchfield,et al.  Attractor vicinity decay for a cellular automaton. , 1993, Chaos.

[48]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .

[49]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[50]  Norbert Wiener,et al.  Cybernetics: Control and Communication in the Animal and the Machine. , 1949 .

[51]  James P. Crutchfield,et al.  Mechanisms of Emergent Computation in Cellular Automata , 1998, PPSN.

[52]  Elwyn R. Berlekamp,et al.  Winning Ways for Your Mathematical Plays, Volume 2 , 2003 .

[53]  A. M. Turing,et al.  Computing Machinery and Intelligence , 1950, The Philosophy of Artificial Intelligence.

[54]  Kari Eloranta,et al.  The dynamics of defect ensembles in one-dimensional cellular automata , 1994 .

[55]  Mats G. Nordahl,et al.  Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[56]  F. H. Adler.  Cybernetics, or Control and Communication in the Animal and the Machine. , 1949 .

[57]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[58]  James Edwin Hanson,et al.  Computational Mechanics of Cellular Automata , 1993 .

[59]  Jan Paredis,et al.  Coevolving Cellular Automata: Be Aware of the Red Queen! , 1997, ICGA.

[60]  S. Gould,et al.  Exaptation—a Missing Term in the Science of Form , 1982, Paleobiology.

[61]  James P. Crutchfield,et al.  A Genetic Algorithm Discovers Particle-Based Computation in Cellular Automata , 1994, PPSN.

[62]  Alvy Ray Smith,et al.  Simple Computation-Universal Cellular Spaces , 1971, JACM.

[63]  H. T. Kung.  Why systolic architectures? , 1982, Computer.

[64]  Nagel.  Particle hopping models and traffic flow theory. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[65]  J. Crutchfield.  Is anything ever new?: considering emergence , 1999 .

[66]  James P. Crutchfield,et al.  Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations , 1993, Complex Syst..

[67]  Péter Gács,et al.  Reliable computation with cellular automata , 1983, J. Comput. Syst. Sci..

[68]  Kenneth Steiglitz,et al.  Embedding Computation in One-Dimensional Automata by Phase Coding Solitons , 1988, IEEE Trans. Computers.

[69]  H. Barlow.  Vision: A computational investigation into the human representation and processing of visual information: David Marr. San Francisco: W. H. Freeman, 1982. pp. xvi + 397 , 1983 .

[70]  Switzerland.,et al.  Cellular automation model of reaction-transport processes , 1993, comp-gas/9312002.

[71]  Jean,et al.  The Computer and the Brain , 1989, Annals of the History of Computing.

[72]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[73]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[74]  H. Fuks.  Solution of the density classification problem with two cellular automata rules , 1997, comp-gas/9703001.

[75]  Land,et al.  No perfect two-state cellular automata for density classification exists. , 1995, Physical review letters.

[76]  Abraham Waksman,et al.  An Optimum Solution to the Firing Squad Synchronization Problem , 1966, Inf. Control..

[77]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[78]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .