71 citations · 167 across the 10 of their papers we have counts for
10 papers
Entropy rate of higher-dimensional cellular automata
François Blanchard, Pierre Tisseur
We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift-commuting isomorphisms; as opposed to the entropy of such CA, it is always…
About a low complexity class of Cellular Automata
Pierre Tisseur
Extending to all probability measures the notion of m-equicontinuous cellular automata introduced for Bernoulli measures by Gilman, we show that the entropy is null if m is an inva…
On a zero speed sensitive cellular automaton
Xavier Bressaud, Pierre Tisseur
Using an unusual, yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at asymptotically null speed for almost all c…
Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata
Cristian Coletti, Pierre Tisseur
We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended v…
Equalities, inequalities between density flow, spatial and temporal entropies of cellular automata
Pierre Tisseur
Defining the density flow of perturbations moving at a given speed for cellular automata, we establish equalities and inequalities between the measurable entropy of a cellular auto…
Density of periodic points, invariant measures and almost equicontinuous points of cellular automata
Pierre Tisseur
Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations o…