Topological dynamics of one-dimensional cellular automata

1 Glossary Almost equicontinuous CA has an equicontinuous configuration. Attractor: omega-limit of a clopen invariant set. Blocking word interrupts information flow. Closing CA: distinct asymptotic configurations have distinct images. Column subshift: columns in space-time diagrams. Cross section: one-sided inverse map. ∗Université de Nice Sophia Antipolis, Département d’Informatique, Parc Valrose, F-06108 Nice Cedex 2, France & Center for Theoretical Study, Academy of Sciences and Charles University in Prague, Jilská 1, CZ-11000 Praha 1, Czechia

[1]  J. Banks,et al.  On Devaney's definition of chaos , 1992 .

[2]  Prevalence of odometers in cellular automata , 2005, math/0511030.

[3]  Pietro Di Lena.  Decidable and computational properties of cellular automata , 2007 .

[4]  Karl-Fredrik Berggren,et al.  Quantum cellular automata - Theory, experimentation and prospects , 2006 .

[5]  那須 正和.  Textile systems for endomorphisms and automorphisms of the shift , 1995 .

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

[7]  Mike Boyle,et al.  Periodic points for onto cellular automata , 1999 .

[8]  Kenichi Morita,et al.  Reversible Cellular Automata , 2009, Encyclopedia of Complexity and Systems Science.

[9]  Lyman P. Hurd,et al.  Recursive Cellular Automata Invariant Sets , 1990, Complex Syst..

[10]  Petr Kůrka.  On the measure attractor of a cellular automaton , 2005 .

[11]  Petr Kůrka,et al.  Topological and symbolic dynamics , 2003 .

[12]  Properties of the directional entropy function for cellular automata , 1988 .

[13]  Ethan Akin,et al.  When is a Transitive Map Chaotic , 1996 .

[14]  Eric Goles,et al.  Dynamics of complex interacting systems , 1996 .

[15]  Petr Kurka,et al.  A Search Algorithm for the Maximal Attractor of a Cellular Automaton , 2007, STACS.

[16]  J. Neumann.  The General and Logical Theory of Au-tomata , 1963 .

[17]  Mathieu Sablik.  Etude de l'action conjointe d'un automate cellulaire et du décalage : une approche topologique et ergodique , 2006 .

[18]  Pierre Tisseur,et al.  Some properties of cellular automata with equicontinuity points , 2000 .

[19]  Bruno Codenotti,et al.  TRANSITIVE CELLULAR AUTOMATA ARE SENSITIVE , 1996 .

[20]  E. Coven.  Topological entropy of block maps , 1980 .

[21]  Enrico Formenti,et al.  Subshift attractors of cellular automata , 2007 .

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

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

[24]  Douglas Lind,et al.  An Introduction to Symbolic Dynamics and Coding , 1995 .

[25]  P. Kurka.  Languages, equicontinuity and attractors in cellular automata , 1997, Ergodic Theory and Dynamical Systems.

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

[27]  T. Moothathu.  STUDIES IN TOPOLOGICAL DYNAMICS WITH EMPHASIS ON CELLULAR AUTOMATA , 2006 .

[28]  Paul Manneville,et al.  Cellular Automata and Modeling of Complex Physical Systems , 1989 .

[29]  Eric Goles,et al.  Cellular automata, dynamical systems, and neural networks , 1994 .

[30]  Petr Kurka.  Cellular Automata with an Infinite Number of Subshift Attractors , 2007, Complex Syst..

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

[32]  Mike Boyle,et al.  Jointly Periodic Points in Cellular Automata: Computer Explorations and Conjectures , 2007, Exp. Math..

[33]  Masakazu Nasu.  Textile systems and one-sided resolving automorphisms and endomorphisms of the shift , 2008, Ergodic Theory and Dynamical Systems.

[34]  Klaus Sutner,et al.  Computation theory of cellular automata , 1998 .

[35]  Jacques Demongeot,et al.  Dynamical Systems and Cellular Automata , 1985 .

[36]  D. Lind,et al.  Expansive Subdynamics , 1996 .

[37]  Mike Hurley.  Attractors in cellular automata , 1990 .

[38]  Mathieu Sablik.  Directional dynamics for cellular automata: A sensitivity to initial condition approach , 2008, Theor. Comput. Sci..

[39]  Petr Kurka,et al.  Dynamics of Cellular Automata in Non-compact Spaces , 2009, Encyclopedia of Complexity and Systems Science.

[40]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[41]  Cristopher Moore,et al.  New constructions in cellular automata , 2003 .

[42]  H. Gutowitz.  Cellular automata: theory and experiment : proceedings of a workshop , 1991 .

[43]  François Blanchard,et al.  Dynamical Behaviour of Coven's Aperiodic Cellular Automata , 1996, Theor. Comput. Sci..

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

[45]  John W. Milnor,et al.  On the Entropy Geometry of Cellular Automata , 1988, Complex Syst..

[46]  Symbolic dynamics , 2008, Scholarpedia.

[47]  K. Culík,et al.  Computation theoretic aspects of cellular automata , 1990 .