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Abbreviations
- Algorithmic complexity of object x :
-
shortest program for outputting a description for x(w.r.t. a universal representation system)
- Equicontinuity:
-
all points are equicontinuity points (in compact settings)
- Equicontinuity point:
-
a point for which the orbits of nearby points remain close
- Expansivity:
-
from two distinct points orbits eventually separate
- Incompressible word:
-
a word for which the shortest program outputting it has “almost” thesame length as the word itself
- Injectivity:
-
the next state function is injective
- Kolmogorov complexity:
-
see “algorithmic complexity”
- Rich configuration:
-
a configuration that contains all possible finite patterns overa given alphabet
- Sensitivity to initial conditions:
-
for any point x there exist arbitrary close pointswhose orbits eventually separate from the orbit of x
- Surjectivity:
-
the next state function is surjective
- Transitivity:
-
there always exist points that eventually move from any arbitraryneighborhood to any other
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Acknowledgments
This work has been partially supported by the ANR Blanc Project “Sycomore”.
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Cervelle, J., Formenti, E. (2009). Algorithmic Complexity and Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_17
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