The Entropy of Linear Cellular Automata with Respect to Any Bernoulli Measure
Hasan Akin
Department of Mathematics
Arts and Science Faculty
Harran University, Sanliurfa, 63120, Turkey
akinhasan@harran.edu.tr
Abstract
This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) 
, generated by a bipermutative local rule 
(m ≥ 2 and l, 
), with respect to the Bernoulli measure 
on 
defined by a probability vector 
. We prove that the measure entropy of the one-dimensional LCA 
with respect to any Bernoulli measure 
is equal to 
.
