Asynchronous cellular automata and dynamical properties

In this article the dynamical behaviour of asynchronous cellular automata (CA) is formally studied. Classical CA properties as surjectivity, injectivity, sensitivity, expansivity, transitivity, dense periodic orbits and equicontinuity have been adapted to the asynchronous case. We also deal with stability of properties with respect to perturbations on some update sequences which produce a significant dynamical behaviour.

[1]  Nazim Fatès,et al.  Fully asynchronous behavior of double-quiescent elementary cellular automata , 2006, Theor. Comput. Sci..

[2]  T. E. Ingerson,et al.  Structure in asynchronous cellular automata , 1984 .

[3]  Gilles Bernot,et al.  HSIM: a simulation programme to study large assemblies of proteins , 2002 .

[4]  Damien Regnault,et al.  Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority , 2007, Theor. Comput. Sci..

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

[6]  Petr Kurka,et al.  Cellular Automata Dynamical Systems , 2012, Handbook of Natural Computing.

[7]  Petr Kůrka,et al.  Topological dynamics of one-dimensional cellular automata , 2007 .

[8]  Nazim Fatès,et al.  Fully Asynchronous Behavior of Double-Quiescent Elementary Cellular Automata , 2005, MFCS.

[9]  Nazim Fatès,et al.  An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata , 2004, Complex Syst..

[10]  Santanu Chattopadhyay,et al.  Additive cellular automata : theory and applications , 1997 .

[11]  Henryk Fukś.  eb 2 00 3 Non-deterministic density classification with diffusive probabilistic cellular automata , .

[12]  Masayuki Kimura,et al.  Injectivity and Surjectivity of Parallel Maps for Cellular Automata , 1979, J. Comput. Syst. Sci..

[13]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[14]  Luigi Acerbi,et al.  Shifting and Lifting of Cellular Automata , 2007 .

[15]  Rodney A. Brooks,et al.  Asynchrony induces stability in cellular automata based models , 1994 .

[16]  Gianpiero Cattaneo,et al.  Solution of some conjectures about topological properties of linear cellular automata , 2004, Theor. Comput. Sci..

[17]  B. Schönfisch,et al.  Synchronous and asynchronous updating in cellular automata. , 1999, Bio Systems.

[18]  Luigi Acerbi,et al.  Conservation of some dynamical properties for operations on cellular automata , 2009, Theor. Comput. Sci..

[19]  Enrico Formenti,et al.  On the directional dynamics of additive cellular automata , 2009, Theor. Comput. Sci..

[20]  Gianpiero Cattaneo,et al.  Non-uniform Cellular Automata , 2009, LATA.

[21]  Damien Regnault,et al.  Abrupt Behaviour Changes in Cellular Automata under Asynchronous Dynamics , 2006 .

[22]  Nazim Fatès,et al.  Asynchronous Behavior of Double-Quiescent Elementary Cellular Automata , 2006, LATIN.

[23]  Pierre Guillon,et al.  Sand automata as cellular automata , 2009, Theor. Comput. Sci..

[24]  Enrico Formenti,et al.  Decidable Properties of 2D Cellular Automata , 2008, Developments in Language Theory.

[25]  Gianpiero Cattaneo,et al.  Chaotic Subshifts and Related Languages Applications to one-dimensional Cellular Automata , 2002, Fundam. Informaticae.

[26]  Alberto Dennunzio,et al.  A Predator-Prey Cellular Automaton with Parasitic Interactions and Environmental Effects , 2008, Fundam. Informaticae.