The Entropy of Linear Cellular Automata with Respect to Any Bernoulli Measure
نویسنده
چکیده
This paper deals with the measure-theoretical entropy of a linear cellular automaton (LCA) Tf @-l,rD :m Ø m , generated by a bipermutative local rule f Ix-l, ... , xrM ⁄i-l r ai xi Hmod mL (m ¥ 2 and l, r œ +), with respect to the Bernoulli measure mp on m defined by a probability vector p Ip0, p1, ... , pm-1M. We prove that the measure entropy of the one-dimensional LCA Tf @-l,rD with respect to any Bernoulli measure mp is equal to Hl + rL ⁄i0 m-1 pi log pi.
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ورودعنوان ژورنال:
- Complex Systems
دوره 18 شماره
صفحات -
تاریخ انتشار 2009