CSR 2012: Computer Science – Theory and Applications pp 266-277 | Cite as
Space-Bounded Kolmogorov Extractors
Conference paper
Abstract
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.
Keywords
Marked Cell Ordinal Number Kolmogorov Complexity Good Seed Balance Property
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 3.Hitchcock, J., Pavan, A., Vinodchandran, N.: Kolmogorov complexity in randomness extraction. Electronic Colloquium on Computational Complexity (ECCC) 16, 71 (2009)Google Scholar
- 4.Musatov, D.: Improving the Space-Bounded Version of Muchnik’s Conditional Complexity Theorem via “Naive” Derandomization. In: Kulikov, A., Vereshchagin, N. (eds.) CSR 2011. LNCS, vol. 6651, pp. 64–76. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 5.Nisan, N., Wigderson, A.: Hardness vs. Randomness. Journal of Computer and System Sciences 49(2), 149–167 (1994)MathSciNetMATHCrossRefGoogle Scholar
- 6.Romashchenko, A.: Pseudo-random Graphs and Bit Probe Schemes with One-Sided Error. In: Kulikov, A., Vereshchagin, N. (eds.) CSR 2011. LNCS, vol. 6651, pp. 50–63. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 7.Shaltiel, R.: An Introduction to Randomness Extractors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 21–41. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 8.Viola, E.: Randomness buys depth for approximate counting. In: Proceedings of IEEE FOCS 2011, pp. 230–239 (2011)Google Scholar
- 9.Zimand, M.: Two Sources Are Better Than One for Increasing the Kolmogorov Complexity of Infinite Sequences. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) CSR 2008. LNCS, vol. 5010, pp. 326–338. Springer, Heidelberg (2008)CrossRefGoogle 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
- 11.Zimand, M.: Impossibility of Independence Amplification in Kolmogorov Complexity Theory. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 701–712. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 12.Zimand, M.: Possibilities and impossibilities in Kolmogorov complexity extraction. Sigact News 41(4), 74–94 (2010)MathSciNetGoogle 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
- 14.Zimand, M.: On the Optimal Compression of Sets in PSPACE. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 65–77. Springer, Heidelberg (2011)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2012