Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
Regular Article: The surjectivity problem for 2D cellular automata
Proceedings of the 30th IEEE symposium on Foundations of computer science
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
Ergodicity, transitivity, and regularity for linear cellular automata over Zm1
Theoretical Computer Science
Kolmogorov complexity and cellular automata classification
Theoretical Computer Science
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Stability of subshifts in cellular automata
Fundamenta Informaticae - Special issue on cellular automata
Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Journal of Computer and System Sciences
IEEE Transactions on Information Theory
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We study the ability of discrete dynamical systems to transform/ generate randomness in cellular spaces. Thus, we endow the space of bi-infinite sequences by a metric inspired by information distance (defined in the context of Kolmogorov complexity or algorithmic information theory). We prove structural properties of this space (non-separability, completeness, perfectness and infinite topological dimension), which turn out to be useful to understand the transformation of information performed by dynamical systems evolving on it. Finally, we focus on cellular automata and prove a dichotomy theorem: continuous cellular automata are either equivalent to the identity or to a constant one. This means that they cannot produce any amount of randomness.