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On the Ergodic Properties of Certain Additive Cellular Automata over Z_m [article]

Hasan Akin
2005 arXiv   pre-print
Z_m.  ...  In this paper, we investigate some ergodic properties of Z^2-actions T_p,n generated by an additive cellular automata and shift acting on the space of all doubly -infinitive sequences taking values in  ...  In this paper, we shall restrict our attention to additive cellular automata over Z m .  ... 
arXiv:math/0511261v1 fatcat:fyqcnw6vujejfkfff7gfuia5qm

On the topological directional entropy

Hasan Akın
2009 Journal of Computational and Applied Mathematics  
We generalize the results obtained by Akı n [The topological entropy of invertible cellular automata, J. Comput. Appl.  ...  T_f[l, r]: Z^Z_m→Z^Z_m which are given by T_f[l, r](x) =(y_n)_ -∞^∞, y_n = f(x_n+l, ..., x_n+r) = ∑_i=l^rλ_ix_i+n(mod m), x=(x_n)_ n=-∞^∞∈Z^Z_m, and f: Z_m^r-l+1→Z_m, over the ring Z_m (m ≥ 2), and the  ...  Introduction Cellular automata (CA), initialed by Ulam and von Neumann, has been systematically studied by Hedlund from purely mathematical point of view [12] .  ... 
doi:10.1016/j.cam.2008.08.012 fatcat:hjnlsvs6ljhgfdjowjh27crc5a

On the dynamical behaviour of linear higher-order cellular automata and its decidability

Alberto Dennunzio, Enrico Formenti, Luca Manzoni, Luciano Margara, Antonio E. Porreca
2019 Information Sciences  
Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing  ...  We also prove that linear HOCA of size memory n over Z_m form a class that is indistinguishable from a specific subclass of LCA over Z_m^n.  ...  cellular automata over m .  ... 
doi:10.1016/j.ins.2019.02.023 fatcat:oeazglfuorh4dgta33yefe7pna

On the Bernoulli automorphism of reversible linear cellular automata

Chih-Hung Chang, Huilan Chang
2016 Information Sciences  
This investigation studies the ergodic properties of reversible linear cellular automata over Z_m for m ∈N.  ...  linear cellular automata.  ...  cellular automata over Z m .  ... 
doi:10.1016/j.ins.2016.01.062 fatcat:i23c4afwhbcjneptbrgdpgf3lu

The Measure-Theoretical Entropy of a Linear Cellular Automata with respect to a Markov Measure [article]

Hasan Akin
2006 arXiv   pre-print
In this paper we study the measure-theoretical entropy of the one-dimensional linear cellular automata (CA hereafter) T_f[-l,r], generated by local rule f(x_-l,...  ...  ,x_r)= ∑_i=-l^rλ_ix_i(mod m), where l and r are positive integers, acting on the space of all doubly infinite sequences with values in a finite ring Z_m, m ≥ 2, with respect to a Markov measure.  ...  In [10] , Mass and Martinez have studied the dynamics of Markov measures by a particular linear cellular automata (LCA).  ... 
arXiv:math/0609015v1 fatcat:2mxuyt3voragtlqoedugfplqkm

MFCS'98 Satellite Workshop on Cellular Automata

Thomas Worsch, Roland Vollmar, [Hrsg.]
1998
Margara: Topological Mixing and Denseness of Periodic Orbits for Linear Cellular Automata over Z_m B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata K. Morita, K.  ...  Sutner: Computation Theory of Cellular Automata  ...  Linear cellular automata over Z m . Journal of Computer and System Sciences, 27:125{140, 1983. 11] J. Kari. Rice's theorem for the limit set of cellular automata.  ... 
doi:10.5445/ir/33798 fatcat:gm2kadutjrfddhm5f2dzctmiia