How to get more mileage from randomness extractors

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn 2006, Issue , 2006, Pages 46-60

  Shaltiel, Ronen ^a  

^a UNIVERSITY OF HAIFA   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; CORRELATION METHODS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION;

INDEPENDENT DISTRIBUTIONS; RANDOMNESS EXTRACTOR; SOURCE DISTRIBUTION;

RANDOM NUMBER GENERATION;

EID: 34247504711     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2006.24     Document Type: Conference Paper

References (40)

1. B. Barak, R. Impagliazzo, and A. Wigderson. Extracting randomness from few independent sources. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pages 384-393, 2004.
2. B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson. Simulating independence: New constructions of condenesers, ramsey graphs, dispersers, and extractors. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 1-10, 2005.
3. M. Bellare, O. Goldreich, and E. Petrank. Uniform generation of NP-witnesses using an NP-oracle. INFCTRL: Information and Computation (formerly Information and Control), 163, 2000.
4. M. Ben-Or and N. Linial. Collective coin flipping. ADVCR: Advances in Computing Research, 5:91-115, 1989.
5. M. Blum. Independent unbiased coin flips from a correlated biased source: a finite state Markov chain. In Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, pages 425-433, 1984.
6. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM Journal on Computing, 17(2):230-261, Apr. 1988.
7. B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, and R. Smolensky. The bit extraction problem or t-resilient functions. In Proceedings of the 26th Annual. IEEE Symposium on Foundations of Computer Science, pages 396-407, 1985.
8. A. Cohen and A. Wigderson. Dispersers, deterministic amplification, and weak random sources. In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, pages 14-25, 1989.
9. Y. Dodis, A. Elbaz, R. Oliviera, and R. Raz. Improved randomnness extractors from two independent sources. In Proceedings of thw 8th International Workshop on Randomization and Computation, 2004.
10. A. Elbaz. Improved constructions for extracting quasi-random bits from sources of weak randomness. Master's thesis, Weizmann institute, August 2003.
11. A. Gabizon and R. Raz. Deterministic extractors for affine sources over large fields. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2005.
12. A. Gabizon, R. Raz, and R. Shaltiel. Deterministic extractors for bit-fixing sources by obtaining an independent seed. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2004.
13. O. Goldreich. A sample of samplers - a computational perspective on sampling. Electronic Colloquium on Computational Complexity (ECCC), 4(20), 1997.
14. O. Goldreich and A. Wigderson. Tiny families of functions with random properties: A quality-size trade-off for hashing. RSA: Random Structures and Algorithms, 11, 1997.
15. M. R. Jerrum, L. G. Valiant, and V. V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science, 43(2-3):169-188, 1986.
16. J. Kamp and D. Zuckerman. Deterministic extractors for bit-fixing sources and exposure-resilient cryptography. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pages 92-101, 2003.
17. C. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: Optimal up to constant factors. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing, 2003.
18. R. Motwani and P. Raghavan. Randomized algorithms. Cambridge University press, 1995.
19. N. Nisan. Extracting randomness: How and why: A survey. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 44-58, 1996.
20. N. Nisan and A. Ta-Shma. Extracting randomness: A survey and new constructions. Journal of Computer and System Sciences, 58(1): 148-173, 1999.
21. N. Nisan and A. Wigderson. Hardness vs randomness. Journal of Computer and System Sciences, 49(2): 149-167, Oct. 1994.
22. N. Nisan and D. Zuckerman. Randomness is linear in space. Journal of Computer and System Sciences, 52(1):43-52, 1996.
23. J. Radhakrishnan and A. Ta-Shma. Bounds for dispersers, extractors, and depth-two superconcentrators. SIAM Journal on Discrete Mathematics, 13(1):2-24, Feb. 2000.
24. R. Raz. Extractors with weak random seeds. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 11-20, 2005.
25. R. Raz, O. Reingold, and S. Vadhan. Error reduction for extractors. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pages 425-433, 1999.
26. O. Reingold, S. Vadhan, and A. Wigderson. Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, 2000.
27. M. Santha and U. V. Vazirani. Generating quasi-random sequences from semi-random sources. Journal of Computer and System Sciences, 33:75-87, 1986.
28. R. Shaltiel. Recent developments in explicit constructions of extractors. Bulletin of the EATCS, 77:67-95, 2002.
29. R. Shaltiel and C. Umans. Simple extractors for all minentropies and a new pseudo-random generator. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, 2001.
30. L. Stockmeyer. The complexity of approximate counting. In ACM, editor, Proceedings of the 15th Annual ACM Symposium on Theory of Computing, 1983.
31. L. Trevisan. Construction of extractors using pseudorandom generators. In Proceedings of the 31st ACM Symposium on Theory of Computing, 1999.
32. L. Trevisan and S. Vadhan. Extracting randomness from samplable distributions. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 32-42, 2000.
33. E. Upfal and M. Mitzenmacher. Probability and comnputing. Cambridge university press, 2005.
34. S. Vadhan. Randomness extractors and their many guises. In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, pages 9-12, 2002.
35. U. Vazirani. Efficient considerations in using semi-random sources. In Proceedings of the 19th Annual ACM Symposium on the Theory of Computing, pages 160-168, 1987.
36. U. Vazirani. Strong communication complexity or generating quasi-random sequences from two communicating semi-random sources. Combinatorica, 7:375-392, 1987.
37. U. V. Vazirani and V. V. Vazirani. Random polynomial time is equal to semi-random polynomial time. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, pages 417-428, 1985.
38. J. von Neumann. Various techniques used in connection with random digits. Applied Math Series, 12:36-38, 1951.
39. D. Zuckerman. General weak random sources. In Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, pages 534-543, 1990.
40. D. Zuckerman. Simulating BPP using a general weak random source. Algorithmica, 16(4/5):367-391, Oct./Nov. 1996.