Pseudorandom bit generators that fool modular sums

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5687 LNCS, Issue , 2009, Pages 615-630

  Lovett, Shachar ^a   Reingold, Omer ^a   Trevisan, Luca ^b   Vadhan, Salil ^c  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRUCTION WORKS; DIRECTED GRAPHS; FIRST CONSTRUCTIONS; FOLLOWING PROBLEM; GRAPH SQUARING; PSEUDO RANDOM; PSEUDORANDOM BIT GENERATOR;

COMBINATORIAL OPTIMIZATION; GRAPH THEORY; SEED; TECHNICAL PRESENTATIONS;

APPROXIMATION ALGORITHMS;

EID: 70449733050     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03685-9_46     Document Type: Conference Paper

References (27)

1. [AIK+] Ajtai, M., Iwaniec, H., Komlós, J., Pintz, J., Szemerédi, E.: Construction of a thin set with small Fourier coefficients. Bull. London Math. Soc. 22(6), 583-590 (1990)
2. [AKS] Ajtai, M., Komlós, J., Szemerédi, E.: Deterministic Simulation in LOGSPACE. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, New York City, pp. 132-140 (1987)
3. [AGHP] Alon, N., Goldreich, O., Håstad, J., Peralta, R.: Simple constructions of almost k-wise independent random variables. Random Structures & Algorithms 3(3), 289-304 (1992)
4. [AM] Alon, N., Mansour, Y.: ε-discrepancy sets and their application for interpolation of sparse polynomials. Information Processing Letters 54(6), 337-342 (1995)
5. [AR] Alon, N., Roichman, Y.: Random Cayley graphs and expanders. Random Structures Algorithms 5(2), 271-284 (1994)
6. [BNS] Babai, L., Nisan, N., Szegedy, M.: Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. Journal of Computer and System Sciences, 204-232 (1989)
7. [BR] Bellare, M., Rompel, J.: Randomness-Efficient Oblivious Sampling. In: 35th Annual Symposium on Foundations of Computer Science, Santa Fe, New Mexico, pp. 276-287. IEEE, Los Alamitos (1994)
8. [BSVW] Ben-Sasson, E., Sudan, M., Vadhan, S., Wigderson, A.: Randomness-efficient low degree tests and short PCPs via epsilon-biased sets. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 612-621. ACM, New York (2003) (electronic)
9. [BV] Bogdanov, A., Viola, E.: Pseudorandom Bits for Polynomials. In: FOCS, pp. 41-51. IEEE Computer Society Press, Los Alamitos (2007)
10. [DGJ+] Diakonikolas, I., Gopalan, P., Jaiswal, R., Servedio, R.A., Viola, E.: Bounded Independence Fools Halfspaces. CoRR abs/0902.3757 (2009)
11. [EGL+] Even, G., Goldreich, O., Luby, M., Nisan, N., Velič ković, B.: Efficient approximation of product distributions. Random Structures Algorithms 13(1), 1-16 (1998)
12. [HPS] Håstad, J., Phillips, S., Safra, S.: A well-characterized approximation problem. Information Processing Letters 47(6), 301-305 (1993)
13. [INW] Impagliazzo, R., Nisan, N., Wigderson, A.: Pseudorandomness for Network Algorithms. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on the Theory of Computing, Montréal, Québec, Canada, pp. 356-364 (1994)
14. [Kat] Katz, N.M.: An estimate for character sums. Journal of the American Mathematical Society 2(2), 197-200 (1989)
15. [Lov] Lovett, S.: Unconditional pseudorandom generators for low degree polynomials. In: Ladner, R.E., Dwork, C. (eds.) STOC, pp. 557-562. ACM, New York (2008)
16. [MZ] Meka, R., Zuckerman, D.: Small-Bias Spaces for Group Products. In: Dinur, I., et al. (eds.) APPROX and RANDOM 2009. LNCS, vol. 5687, Springer, Heidelberg (2009)
17. 0. Random Structures Algorithms 29(1), 56-81 (2006)
18. [MNN] Motwani, R., Naor, J., Naor, M.: The probabilistic method yields deterministic parallel algorithms. Journal of Computer and System Sciences 49(3), 478-516 (1994)
19. [NN] Naor, J., Naor, M.: Small-Bias Probability Spaces: Efficient Constructions and Applications. SIAM Journal on Computing 22(4), 838-856 (1993)
20. [Nao] Naor, M.: Constructing Ramsey graphs from small probability spaces. Technical Report RJ 8810, IBM Research Report (1992)
21. [Nis] Nisan, N.: Pseudorandom generators for space-bounded computation. Combinatorica 12(4), 449-461 (1992)
22. [RS] Rabani, Y., Shpilka, A.: Explicit construction of a small epsilon-net for linear threshold functions. In: Mitzenmacher, M. (ed.) STOC, pp. 649-658. ACM, New York (2009)
23. [RSW] Razborov, A., Szemerédi, E., Wigderson, A.: Constructing small sets that are uniform in arithmetic progressions. Combinatorics, Probability and Computing 2(4), 513-518 (1993)
24. [RTV] Reingold, O., Trevisan, L., Vadhan, S.: Pseudorandom Walks In Regular Digraphs and the RL vs. L problem. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, STOC 2006, May 21-23 (2006); Preliminary version on ECCC (February 2005)
25. [RV] Rozenman, E., Vadhan, S.: Derandomized Squaring of Graphs. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX and RANDOM 2005. LNCS, vol. 3624, pp. 436-447. Springer, Heidelberg (2005)
26. 3/2). Journal of Computer and System Sciences 58, 376-403 (1999)
27. [Vio] Viola, E.: The Sum of d Small-Bias Generators Fools Polynomials of Degree d. In: IEEE Conference on Computational Complexity, pp. 124-127. IEEE Computer Society, Los Alamitos (2008)