The geometry of fractal sets
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
A Kolmogorov complexity characterization of constructive Hausdorff dimension
Information Processing Letters
A Shift-Invariant Metric on Szz Inducing a Non-trivial Tolology
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Characterization of Sensitive Linear Cellular Automata with Respect to the Counting Distance
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Dimension in Complexity Classes
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Geometry and dynamics of the besicovitch and weyl spaces
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
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We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance induces a distance on the set of shift-invariant measures and on the whole space of measures, and we prove that in these spaces also, cellular automata cannot be expansive nor transitive.