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- W1788851907 abstract "In this paper we study the measure-theoretical entropy of the one-dimensional linear cellular automata (CA hereafter) $T_{f[-l,r]}$, generated by local rule $f(x_{-l},...,x_{r})= sumlimits_{i=-l}^{r}lambda_{i}x_{i}(text{mod} m)$, where $l$ and $r$ are positive integers, acting on the space of all doubly infinite sequences with values in a finite ring $mathbb{Z}_{m}$, $m geq 2$, with respect to a Markov measure. We prove that if the local rule $f$ is bipermutative, then the measure-theoretical entropy of linear CA $T_{f[-l,r]}$ with respect to a Markov measure $mu_{pi P}$ is $ h_{mu_{pi P}}(T_{f[-l,r]})=-(l+r)sumlimits_{i,j=0}^{m-1}p_ip_{ij}text{log} p_{ij}.$" @default.
- W1788851907 created "2016-06-24" @default.
- W1788851907 creator A5036918460 @default.
- W1788851907 date "2006-09-01" @default.
- W1788851907 modified "2023-09-29" @default.
- W1788851907 title "The Measure-Theoretical Entropy of a Linear Cellular Automata with respect to a Markov Measure" @default.
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