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On the Ergodic Properties of Certain Additive Cellular Automata over Z_m
[article]
2005
arXiv
pre-print
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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
2009
Journal of Computational and Applied Mathematics
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2008 pre-print arXiv:0802.0953v1 fatcat:gw3hkoylbbdqjjbwvkurzldrcq
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
2019
Information Sciences
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2019 pre-print arXiv:1902.06775v1 fatcat:cthpli5vpndfxah2klteym4nz4
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
2016
Information Sciences
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2015 pre-print arXiv:1503.05999v2 fatcat:msth5pyeh5e43nwobzznqkjg6uOther Versions
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]
2006
arXiv
pre-print
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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
1998
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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