An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
On a complexity of the formula A∨B⇒C
Theoretical Computer Science - Special issue Kolmogorov complexity
Independent minimum length programs to translate between given strings
Theoretical Computer Science
Nearly Optimal Language Compression Using Extractors
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
IEEE Transactions on Information Theory
Independent minimum length programs to translate between given strings
Theoretical Computer Science
Nonreducible Descriptions for the Conditional Kolmogorov Complexity
Problems of Information Transmission
Individual communication complexity
Journal of Computer and System Sciences
Information distance from a question to an answer
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
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
Variations on Muchnik's Conditional Complexity Theorem
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Stability of properties of Kolmogorov complexity under relativization
Problems of Information Transmission
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Kolmogorov complexity as a language
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Shannon entropy vs. kolmogorov complexity
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Non-reducible descriptions for conditional kolmogorov complexity
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
| Hi-index | 5.23 |
Let x and y be binary strings. We prove that there exists a program p of size about K(x|y) that maps y tox and has small complexity when x is known (K(p|x)0)*#8776;0). Having in mind the parallelism between Shannon information theory and algorithmic information theory, one can say that this result is parallel to Wolf-Slepian and Körner-Csiszar-Marton theorems, see (I. Csiszar and J. Körner, Information theory, Coding Theorems for Discrete Memoryless Systems, Akadémiai Kiadó, Budapest, 1981). We show also that for any three stringsx,y,z of length at most n the length of the shortest program p that maps both y and z to x (i.e., p(y)=p(z)=x) equals max(K(x|y),K(x|z)+O(logn.