Abstract
We prove that the natural extension of the (measure preserving) map T:S Z → S Z (1 < ¦S¦ < ∞) defined by ( Tx) i = F( x i + l ,…, x i + r ), x ε S Z , i ε Z , where F is right (respectively, left) permutative, is a K-automorphism, unless r = 0 (respectively, l = 0). From this we conclude that, except for the identity and the involution, the Wolfram's elementary cellular automata have the K-property whenever they are onto.
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