m-Asynchronous Cellular Automata

A new model for the study of ACA dynamical behavior has been introduced. The classical properties of injectivity, surjectivity and expansivity have been adapted to the new setting. Preliminary results show that the injectivity is almost always equal to surjectivity and that both property are almost always implied by expansivity.

[1]  Henning S. Mortveit,et al.  Order Independence in Asynchronous Cellular Automata , 2008, J. Cell. Autom..

[2]  Paul R. Halmos Inverses and Composites , 1974 .

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

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

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

[8]  Luciano Margara,et al.  Expansivity, Permutivity, and Chaos for Cellular Automata , 1998, Theory of Computing Systems.

[9]  Luca Manzoni Asynchronous cellular automata and dynamical properties , 2012, Natural Computing.

[10]  L. Kier,et al.  Cellular automata modeling of chemical systems : a textbook and laboratory manual , 2005 .

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

[12]  Marcos Kiwi,et al.  LATIN 2006: Theoretical Informatics , 2006, Lecture Notes in Computer Science.

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

[14]  Grégoire Nicolis,et al.  Synchronous versus asynchronous dynamics in spatially distributed systems , 1994 .

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

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

[17]  H. Fuks Nondeterministic density classification with diffusive probabilistic cellular automata. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[19]  Ferdinand Peper,et al.  Delay-insensitive computation in asynchronous cellular automata , 2005, J. Comput. Syst. Sci..

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

[21]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[22]  Henryk Fuks,et al.  Probabilistic cellular automata with conserved quantities , 2003, nlin/0305051.