An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Theoretical Computer Science - Special issue Kolmogorov complexity
Inequalities for Shannon entropy and Kolmogorov complexity
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Information distance from a question to an answer
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
A Random Oracle Does Not Help Extract the Mutual Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Information shared by many objects
Proceedings of the 17th ACM conference on Information and knowledge management
New information distance measure and its application in question answering system
Journal of Computer Science and Technology
Stability of properties of Kolmogorov complexity under relativization
Problems of Information Transmission
Nonapproximability of the normalized information distance
Journal of Computer and System Sciences
Kolmogorov complexity as a language
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Multisource algorithmic information theory
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Information distance and its applications
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
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In this paper we construct a structure R that is a "finite version" of the semi-lattice of Turing degrees. Its elements are strings (technically, sequences of strings) and xy means thatK(x|y)=(conditional Kolmogorov complexity of x relative to y) is small. We construct two elements in R that do not have greatest lower bound. We give a series of examples that show how natural algebraic constructions give two elements that have lower bound 0 (minimal element) but significant mutual information. (A first example of that kind was constructed by Gács-Körner (Problems Control Inform. Theory 2 (1973) 149) using a completely different technique.) We define a notion of "complexity profile" of the pair of elements of R and give (exact) upper and lower bounds for it in a particular case.