Non-uniform cellular automata: Classes, dynamics, and decidability

The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjectivity and injectivity is also established. The final part studies a strong form of equicontinuity property specially suited for non-uniform cellular automata.

[1]  Jarkko Kari,et al.  Tiling Problem and Undecidability in Cellular Automata , 2009, Encyclopedia of Complexity and Systems Science.

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

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

[4]  Enrico Formenti,et al.  Multidimensional cellular automata: closing property, quasi-expansivity, and (un)decidability issues , 2014, Theor. Comput. Sci..

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

[6]  Danail Bonchev,et al.  Modeling Biochemical Networks: A Cellular‐Automata Approach , 2005, Chemistry & biodiversity.

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

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

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

[10]  Enrico Formenti,et al.  2D cellular automata: dynamics and undecidability , 2009 .

[11]  Pietro Di Lena,et al.  On the undecidability of the limit behavior of Cellular Automata , 2010, Theor. Comput. Sci..

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

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

[14]  Giancarlo Mauri,et al.  On the Dynamical Behavior of Chaotic Cellular Automata , 1999, Theor. Comput. Sci..

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

[16]  Atsushi Iwata,et al.  A cellular-automaton-type image extraction algorithm and its implementation using an FPGA , 2002, Asia-Pacific Conference on Circuits and Systems.

[17]  Enrico Formenti,et al.  Chaotic Behavior of Cellular Automata , 2009, Encyclopedia of Complexity and Systems Science.

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

[19]  Sukanta Das,et al.  Non-uniform Cellular Automata , 2014, Theor. Comput. Sci..

[20]  Jarkko Kari,et al.  Reversibility and Surjectivity Problems of Cellular Automata , 1994, J. Comput. Syst. Sci..

[21]  Ludwig Staiger,et al.  Ω-languages , 1997 .

[22]  Klaus Sutner,et al.  De Bruijn Graphs and Linear Cellular Automata , 1991, Complex Syst..

[23]  Enrico Formenti,et al.  Local rule distributions, language complexity and non-uniform cellular automata , 2013, Theor. Comput. Sci..

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

[25]  Enrico Formenti,et al.  Computational Complexity of Rule Distributions of Non-uniform Cellular Automata , 2012, LATA.