On ε-biased generators in NC0

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 2003-January, Issue , 2003, Pages 136-145

  Mossel, E ^a   Shpilka, A ^b   Trevisan, L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Circuits; Computer science; Contracts; National security; Polynomials; Random variables; Research and development

Indexed keywords

COMPUTER SCIENCE; CONTRACTS; NETWORKS (CIRCUITS); POLYNOMIAL APPROXIMATION; POLYNOMIALS; RANDOM VARIABLES;

DISTINGUISHERS; OUTPUT BITS; POLYNOMIAL-TIME; PSEUDORANDOM GENERATORS; RESEARCH AND DEVELOPMENT;

NATIONAL SECURITY;

EID: 84943420062     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.2003.1238188     Document Type: Conference Paper

References (28)

1. N. Alon, M. Capalbo. Explicit Unique-Neighbor Expanders. Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science, pages 73-79, 2000.
2. N. Alon, O. Goldreich, J. Håstad, and R. Peralta. Simple constructions of almost k-wise independent random variables. Random Structures and Algorithms, 3(3):289-304, 1992.
3. P. Beame, R. Karp, T. Pitassi, and M. Saks. On the complexity of unsatisfiability proofs for random k-cnf formulas. In Proceedings of the 30th ACM Symposium on Theory of Computing, 1998.
4. A. Bogdanov, K. Obata, and L. Trevisan. A lower bound for testing 3-colorability in bounded degree graphs. In Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science, pages 93-102, 2002.
5. E. Ben-Sasson and A. Wigderson. Short proofs are narrow: Resolution made simple. Journal of the ACM, 48(2), 2001.
6. M. Capalbo. Explicit Constant-Degree Unique-Neighbor Expanders, 2001.
7. M. Cryan and P. B. Miltersen. On pseudorandom generators in NC0. In Proceedings of MFCS'01, 2001.
8. M. Capalbo, O. Reingold, S. Vadhan and A. Wigderson. Randomness Conductors and Constant-Degree Expansion Beyond the Degree/2 Barrier. Proceedings of the 34th Symposium on the Theory of Computing, 659-668, 2000.
9. O. Goldreich, S. Goldwasser, and S. Micali. How to construct random functions. Journal of the ACM, 33(4):792-807, 1986.
10. O. Goldreich. Candidate one-way functions based on expander graphs. Technical Report TR00-090, ECCC, 2000.
11. M.X. Goemans and D.P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM, 42(6):1115-1145, 1995.
12. J. Håstad. Some optimal inapproximability results. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 1-10, 1997.
13. J. Håstad, R. Impagliazzo, L. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM Journal on Computing, 28(4):1364-1396, 1999.
14. J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, 1979.
15. R. Impagliazzo and M. Naor. Efficient cryptographic schemes provably as secure as subset sum. Journal of Cryptology, 9(4):199-216, 1996.
16. T. Johansson and F. Jonsson. Improved fast correlation attacks on stream ciphers via convolutional codes. In Proceedings of EUROCRYPT'99, 1999.
17. N. Linial, Y. Mansour, and N. Nisan. Constant depth circuits, fourier transform and learnability. Journal of the ACM, 40(3):607-620, 1993.
18. A. Lubotzky, R. Phillips, and P. Sarnak. Ramanujan graphs. Combinatorica, 8:261-277, 1988.
19. C. J. Lu and O. Reingold and S. Vadhan and A. Wigderson Extractors: Optimal Up to Constant Factors. To appear in proceedings of the 35th Annual symposium on the theory of computing (STOC).
20. M. Luby and C. Rackoff. How to construct pseudorandom permutations from pseudorandom functions. SIAM Journal on Computing, 2(17):373-386, 1988.
21. R. Meshulam. Spaces of Hankel matrices over finite fields, Linear Algebra Appl. 218, 73-76, 1995.
22. E. Mossel, R. O'Donnell and R. Servedio (2003) Learning Juntas. To appear in proceedings of the 35th Annual symposium on the theory of computing (STOC).
23. J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications, SIAM Journal on Computing, 22(4):838-856, 1993.
24. R. Roth. Maximum rank array codes and their application to crisscross error correction, IEEE Trans. on Info. Th. 37, 328-336, 1991.
25. J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. Journal of the ACM, 27(4):701-717, 1980.
26. A. Shpilka. On the rigidity of matrices. Manuscript, 2002.
27. U. Vazirani. Randomness, Adversaries and Computation. PhD thesis, University of California, Berkeley, 1986.
28. R. Zippel. Probabilistic algorithms for sparse polynomials. In Symbolic and algebraic computation (EUROSAM '79, Internat. Sympos., Marseille, 1979), pages 216-226. Springer, Berlin, 1979.