Journal of Computer and System Sciences
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of 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
Kakeya Sets, New Mergers and Old Extractors
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
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
Theory of Computing Systems
Pseudo-random graphs and bit probe schemes with one-sided error
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
On the optimal compression of sets in PSPACE
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
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Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with better parameters than explicit constructions do. But the probabilistic method does not give "effective" variants of such theorems, i.e. variants for resource-bounded Kolmogorov complexity. We show that a "naive derandomization" approach of replacing these objects by the output of Nisan-Wigderson pseudo-random generator may give polynomial-space variants of such theorems. Specifically, we improve the preceding polynomial-space analogue of Muchnik's conditional complexity theorem. I.e., for all a and b there exists a program p of least possible length that transforms a to b and is simple conditional on b. Here all programs work in polynomial space and all complexities are measured with logarithmic accuracy instead of polylogarithmic one in the previous work.