An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Conditional complexity and codes
Theoretical Computer Science
Resource-Bounded Kolmogorov Complexity Revisited
SIAM Journal on Computing
Language Compression and Pseudorandom Generators
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Extracting Randomness via Repeated Condensing
SIAM Journal on Computing
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
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
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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Muchnik's theorem about simple conditional descriptions states that for all strings a and b there exists a short program p transforming a to b that has the least possible length and is simple conditional on b . In this paper we present two new proofs of this theorem. The first one is based on the on-line matching algorithm for bipartite graphs. The second one, based on extractors, can be generalized to prove a version of Muchnik's theorem for space-bounded Kolmogorov complexity.