Unraveling simplicity in elementary cellular automata

We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the generality of communication complexity, the perspectives of our method include its application to other natural systems such as neural networks and gene regulatory networks.

[1]  Guillaume Theyssier.  How Common Can Be Universality for Cellular Automata? , 2005, STACS.

[2]  Pierre-Etienne Meunier.  Les automates cellulaires en tant que modèle de complexités parallèles. (Cellular automata as a model of parallel complexities) , 2012 .

[3]  Nicolas Ollinger.  Universalities in cellular automata a (short) survey , 2008, JAC.

[4]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[5]  Erik Winfree,et al.  The program-size complexity of self-assembled squares (extended abstract) , 2000, STOC '00.

[6]  Peter W. Shor,et al.  Quantum Information Theory , 1998, IEEE Trans. Inf. Theory.

[7]  Guillaume Theyssier,et al.  On Factor Universality in Symbolic Spaces , 2010, MFCS.

[8]  James P. Crutchfield,et al.  Computational mechanics of cellular automata: an example , 1997 .

[9]  Matthew J. Patitz,et al.  Intrinsic universality in tile self-assembly requires cooperation , 2013, SODA.

[10]  Matthew Cook,et al.  Universality in Elementary Cellular Automata , 2004, Complex Syst..

[11]  Navot Israeli,et al.  Computational irreducibility and the predictability of complex physical systems. , 2003, Physical review letters.

[12]  Ivan Rapaport,et al.  Cellular automata and communication complexity , 2002, Theor. Comput. Sci..

[13]  Erik D. Demaine,et al.  The Two-Handed Tile Assembly Model is not Intrinsically Universal , 2013, Algorithmica.

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

[15]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[16]  Jarkko Kari.  The Nilpotency Problem of One-Dimensional Cellular Automata , 1992, SIAM J. Comput..

[17]  N. Goldenfeld,et al.  Coarse-graining of cellular automata, emergence, and the predictability of complex systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Cristopher Moore,et al.  Predicting nonlinear cellular automata quickly by decomposing them into linear ones , 1997, patt-sol/9701008.

[19]  Damien Woods,et al.  Intrinsic Universality in Self-Assembly , 2010, Encyclopedia of Algorithms.

[20]  Ruedi Stoop,et al.  A full computation-relevant topological dynamics classification of elementary cellular automata. , 2012, Chaos.

[21]  Jack H. Lutz,et al.  The Tile Assembly Model is Intrinsically Universal , 2011, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[22]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[23]  Turlough Neary,et al.  P-completeness of Cellular Automaton Rule 110 , 2006, ICALP.

[24]  Eric Goles Ch.,et al.  Communication complexity and intrinsic universality in cellular automata , 2011, Theor. Comput. Sci..

[25]  G. A. Hedlund.  Endomorphisms and automorphisms of the shift dynamical system , 1969, Mathematical systems theory.

[26]  Eric Goles Ch.,et al.  Understanding a Non-trivial Cellular Automaton by Finding Its Simplest Underlying Communication Protocol , 2008, ISAAC.

[27]  Guillaume Theyssier,et al.  ON LOCAL SYMMETRIES AND UNIVERSALITY IN CELLULAR , 2009 .

[28]  J. Maxwell,et al.  Theory of Heat , 1892 .

[29]  B. Durand,et al.  The Game of Life: Universality Revisited , 1999 .