Complex Systems

The Entropy of Linear Cellular Automata with Respect to Any Bernoulli Measure Download PDF

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 .