An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Compression of Low Entropy Strings with Lempel--Ziv Algorithms
SIAM Journal on Computing
Information, Randomness and Incompleteness
Information, Randomness and Incompleteness
Mathematics of Information and Coding
Mathematics of Information and Coding
The method of types [information theory]
IEEE Transactions on Information Theory
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The study of weakly chaotic dynamical systems suggests that an important indicator for their classification is the quantity of information that is needed to describe their orbits. The information can be measured by the use of suitable compression algorithms. The algorithms are “optimal” for this purpose if they compress very efficiently zero entropy strings. We discuss a definition of optimality in this sense. We also show that the set of optimal algorithms is not empty, showing a concrete example. We prove that the algorithms which are optimal according to the above definition are suitable to measure the information needed to describe the orbits of the Manneville maps: in these examples the information content measured by these algorithms has the same asymptotic behavior as the algorithmic information content.