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The Topological Directional Entropy of Z^2-actions Generated by Linear Cellular Automata
In this paper we study the topological and metric directional entropy of
-actions by generated additive cellular automata (CA hereafter),
defined by a local rule , , , i.e. the
maps
which are given by , , , and , over the ring , and the shift map acting on compact metric space
, where is a positive integer. Our
main aim is to give an algorithm for computing the topological directional
entropy of the -actions generated by the additive CA and the
shift map. Thus, we ask to give a closed formula for the topological
directional entropy of -action generated by the pair in the direction that can be efficiently and rightly
computed by means of the coefficients of the local rule f as similar to [Theor.
Comput. Sci. 290 (2003) 1629-1646]. We generalize the results obtained by Ak\i
n [The topological entropy of invertible cellular automata, J. Comput. Appl.
Math. 213 (2) (2008) 501-508] to the topological entropy of any invertible
linear CA.Comment: 9 pages. submitte