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

2005
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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 . ...

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On the topological directional entropy

2009
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Journal of Computational and Applied Mathematics
*

We generalize the results obtained by Akı n [The topological entropy of invertible

doi:10.1016/j.cam.2008.08.012
fatcat:hjnlsvs6ljhgfdjowjh27crc5a
*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] . ...##
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On the dynamical behaviour of linear higher-order cellular automata and its decidability

2019
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Information Sciences
*

Higher-order

doi:10.1016/j.ins.2019.02.023
fatcat:oeazglfuorh4dgta33yefe7pna
*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 . ...##
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On the Bernoulli automorphism of reversible linear cellular automata

2016
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Information Sciences
*

This investigation studies the ergodic properties of reversible

doi:10.1016/j.ins.2016.01.062
fatcat:i23c4afwhbcjneptbrgdpgf3lu
*linear**cellular**automata**over**Z_m*for m ∈N. ...*linear**cellular**automata*. ...*cellular**automata**over*Z m . ...##
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The Measure-Theoretical Entropy of a Linear Cellular Automata with respect to a Markov Measure
[article]

2006
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arXiv
*
pre-print

In this paper we study the measure-theoretical entropy of the one-dimensional

arXiv:math/0609015v1
fatcat:2mxuyt3voragtlqoedugfplqkm
*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). ...##
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MFCS'98 Satellite Workshop on Cellular Automata

1998

Margara: Topological Mixing and Denseness of Periodic Orbits for

doi:10.5445/ir/33798
fatcat:gm2kadutjrfddhm5f2dzctmiia
*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*. ...