Space-Bounded Kolmogorov Extractors
An extractor is a function that receives some randomness and either “improves” it or produces “new” randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resource-bounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The utilized technique is “naive” derandomization: we replace random constructions employed by Zimand by pseudo-random ones obtained by Nisan-Wigderson generator.
KeywordsMarked Cell Ordinal Number Kolmogorov Complexity Good Seed Balance Property
Unable to display preview. Download preview PDF.
- 1.Ajtai, M.: Approximate counting with uniform constant-depth circuits. In: Advances in Computational Complexity Theory, pp. 1–20. American Mathematical Society, Providence (1993)Google Scholar
- 2.Fortnow, L., Hitchcock, J., Pavan, A., Vinodchandran, N.V., Wang, F.: Extracting Kolmogorov complexity with applications to dimension zero-one laws. Information and Computation 209(4), 627–636 (2011); Preliminary version appeared in Proceedings of the 33rd International Colloquium on Automata, Languages, and Programming. LNCS, vol. 4051, pp. 335–345 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
- 3.Hitchcock, J., Pavan, A., Vinodchandran, N.: Kolmogorov complexity in randomness extraction. Electronic Colloquium on Computational Complexity (ECCC) 16, 71 (2009)Google Scholar
- 8.Viola, E.: Randomness buys depth for approximate counting. In: Proceedings of IEEE FOCS 2011, pp. 230–239 (2011)Google Scholar
- 10.Zimand, M.: Extracting the Kolmogorov complexity of strings and sequences from sources with limited independence. In: Proceedings 26th STACS, pp. 697–708 (2009)Google Scholar
- 13.Zimand, M.: Symmetry of information and bounds on nonuniform randomness extraction via Kolmogorov extractors. In: Proceedings of 26th IEEE Conference in Computational Complexity, pp. 148–156 (2011)Google Scholar