Randomness conservation inequalities; information and independence in mathematical theories
Information and Control
Logical depth and physical complexity
A half-century survey on The Universal Turing Machine
A half-century survey on The Universal Turing Machine
An almost machine-independent theory of program-length complexity, sophistication, and induction
Information Sciences: an International Journal
Learning to Predict Non-Deterministically Generated Strings
Machine Learning
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Kolmogorov's Structure Functions with an Application to the Foundations of Model Selection
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
IEEE Transactions on Information Theory
Algorithmic Minimal Sufficient Statistic Revisited
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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The Kolmogorov structure function divides the smallest program producing a string in two parts: the useful information present in the string, called sophistication if based on total functions, and the remaining accidental information. We revisit the notion of sophistication due to Koppel, formalize a connection between sophistication and a variation of computational depth (intuitively the useful or nonrandom information in a string), prove the existence of strings with maximum sophistication and show that they encode solutions of the halting problem, i.e., they are the deepest of all strings.