On ε-biased generators in NC0

Random Structures and Algorithms

Volumn 29, Issue 1, 2006, Pages 56-81

  Mossel, Elchanan ^a   Shpilka, Amir ^b,c   Trevisan, Luca ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746430446     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20112     Document Type: Article

References (31)

1. 0, In Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004, pp. 166-175.
2. N. Alon and M. Capalbo, Explicit unique-neighbor expanders, In Proceedings of the 43rd IEEE Symposium on Foundations of Computer Science, 2002, pp. 73-79.
3. N. Alon, O. Goldreich, J. Håstad, and R. Peralta, Simple constructions of almost k-wise independent random variables, Random Struct Algo 3(3) (1992), 289-304.
4. 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, pp. 561-571.
5. 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, 2002, pp. 93-102.
6. E. Ben-Sasson and A. Wigderson, Short proofs are narrow: Resolution made simple, J ACM 48(2) (2001), 146-169.
7. 0, In Proceedings of the 26th Mathematical Foundations of Computer Science, 2001, pp. 272-284.
8. M. Capalbo, O. Reingold, S. Vadhan, and A. Wigderson, Randomness conductors and constant-degree expansion beyond the degree/2 barrier, In Proceedings of the 34th ACM Symposium on the Theory of Computing, 2000, pp. 659-668.
9. O. Goldreich, Three XOR-lemmas - An exposition, Electron Coll Comput Complex 2(56) (1995).
10. O. Goldreich, S. Goldwasser, and S. Micali, How to construct random functions, J ACM 33(4) (1986), 792-807.
11. O. Goldreich, Candidate one-way functions based on expander graphs, Electron Coll Comput Complex TROO-090, 2000.
12. M. X. Goemans and D. P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J ACM 42(6) (1995), 1115-1145.
13. J. Håstad, Some optimal inapproximability results, In Proceedings of the 29th ACM Symposium on Theory of Computing, 1997, pp. 1-10.
14. J. Håstad, R. Impagliazzo, L. Levin, and M. Luby, A pseudorandom generator from any one-way function, SIAM J Comput 28(4) (1999), 1364-1396.
15. J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, 1979.
16. R. Impagliazzo and M. Naor, Efficient cryptographic schemes provably as secure as subset sum, J Cryptol 9(4) (1996), 199-216.
17. T. Johansson and F. Jönsson, Improved fast correlation attacks on stream ciphers via convolutional codes, In Proceedings of International Conference on the Theory and Application of Cryptographic Techniques (EURO-CRYPT), 1999, pp. 347-362.
18. M. Kharitonov, Cryptographic hardness of distribution-specific learning, In Proceedings of 25th ACM Symposium on Theory of Computing, 1993, pp. 372-381.
19. N. Linial, Y. Mansour, and N. Nisan, Constant depth circuits, fourier transform and learnability, J ACM 40(3) (1993), 607-620.
20. A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277.
21. C. J. Lu, O. Reingold, S. Vadhan, and A. Wigderson, Extractors: Optimal up to constant factors, In Proceedings of the 35th ACM Symposium on the Theory of Computing, 2003, pp. 602-611.
22. M. Luby and C. Rackoff, How to construct pseudorandom permutations from pseudorandom functions, SIAM J Comput 2(17) (1988), 373-386.
23. R. Meshulam, Spaces of Hankel matrices over finite fields, Linear Alg Appl 218 (1995), 73-76.
24. E. Mossel, R. O'Donnell, and R. Servedio, Learning Juntas, In Proceedings of the 35th ACM Symposium on the Theory of Computing, 2003, pp. 206-212.
25. 0, In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science, 2003, pp. 136-145.
26. J. Naor and M. Naor, Small-bias probability spaces: Efficient constructions and applications, SIAM J Comput 22(4) (1993), 838-856.
27. R. Roth, Maximum rank array codes and their application to crisscross error correction, IEEE Trans Inform Theory 37 (1991), 328-336.
28. J. T. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, J ACM 27(4) (1980), 701-717.
29. A. Shpilka, On the rigidity of matrices, Manuscript, 2002.
30. U. Vazirani, Randomness, Adversaries and Computation, PhD thesis, University of California, Berkeley, 1986.
31. R. Zippel, Probabilistic algorithms for sparse polynomials, In Symbolic and algebraic computation (EUROSAM), 1979, pp. 216-226.