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
An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Computational depth and reducibility
Theoretical Computer Science
Information and Computation
Compressibility and Resource Bounded Measure
SIAM Journal on Computing
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
SIAM Journal on Computing
Computational depth: concept and applications
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Martingale families and dimension in P
Theoretical Computer Science
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
On the polynomial depth of various sets of random strings
Theoretical Computer Science
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This paper proposes new notions of polynomial depth (called monotone poly depth), based on a polynomial version of monotone Kolmogorov complexity. We show that monotone poly depth satisfies all desirable properties of depth notions i.e., both trivial and random sequences are not monotone poly deep, monotone poly depth satisfies the slow growth law i.e., no simple process can transform a non deep sequence into a deep one, and monotone poly deep sequences exist (unconditionally). We give two natural examples of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov random strings are monotone poly deep.