Hasan Akýn

Arts and Sciences Faculty, Department of Mathematics, Harran University; 63100, Sanliurfa, Turkey.
E-mail: [email protected]

Received: 5 February 2003 / Accepted: 12 June 2003 / Published: 30 June 2003

Abstract: We show that for an additive one-dimensional cellular automata on space of all doubly infinitive sequences with values in a finite set S = {0, 1, 2,..., r-1}, determined by an additive automaton rule f(x_n-k,..., x_n+k) = (mod r), and a -invariant uniform Bernoulli measure m, the measure-theoretic entropy of the additive one-dimensional cellular automata with respect to m is equal to h_m () = 2klog r, where . We also show that the uniform Bernoulli measure is a measure of maximal entropy for additive one-dimensional cellular automata .

Keywords: Cellular Automata, Measure Entropy, Topological Entropy.