Pseudorandom bits for polynomials

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

Volumn , Issue , 2007, Pages 41-51

  Bogdanov, Andrej ^a   Viola, Emanuele ^b  

^a RUTGERS UNIVERSITY   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE FIELDS; NEW APPROACHES; PSEUDO-RANDOM GENERATORS; PSEUDORANDOM BITS;

COMPUTER SCIENCE; FIBER OPTIC CHEMICAL SENSORS; FOUNDATIONS; POLYNOMIAL APPROXIMATION;

POLYNOMIALS;

EID: 46749116820     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2007.4389478     Document Type: Conference Paper

References (21)

1. N. Alon, J. Bruck, J. Naor, M. Naor, and R. M. Roth. Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs. IEEE Transactions on Information Theory, 38(2):509-516, 1992.
2. N. Alon, O. Goldreich, J. Hâstad, and R. Peralta. Simple constructions of almost k-wise independent random variables. Random Structures & Algorithms, 3(3):289-304, 1992.
3. N. Alon, T. Kaufman, M. Krivelevich, S. Litsyn, and D. Ron. Testing low-degree polynomials over GF (2). In Approximation, randomization, and combinatorial optimization, volume 2764 of Lecture Notes in Comput. Sci., pages 188-199. Springer, Berlin, 2003.
4. L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. System Sci., 45(2):204-232, 1992. Twenty-first Symposium on the Theory of Computing (Seattle, WA, 1989).
5. E. Ben-Sasson, M. Sudan, S. Vadhan, and A. Wigderson. 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, pages 612-621 (electronic), New York, 2003. ACM.
6. C. Bertram-Kretzberg and H. Lefmann. Modp-tests, almost independence and small probability spaces. Random Struct. Algorithms, 16(4):293-313, 2000.
7. A. Bogdanov. Pseudorandom generators for low degree polynomials. In STOC'05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 21-30, New York, 2005. ACM.
8. O. Goldreich. Modern cryptography, probabilistic proofs and pseudorandomness, volume 17 of Algorithms and Combinatorics. Springer-Verlag, Berlin, 1999.
9. W. T. Gowers. A new proof of Szemerédi's theorem for arithmetic progressions of length four. Geom. Funct. Anal., 8(3):529-551, 1998.
10. W. T. Gowers. A new proof of Szemerédi's theorem. Geom. Funct. Anal.,11(3):465-588, 2001.
11. 3 norm, 2005. arXiv.org:math/0503014.
12. R. Lidl and H. Niederreiter. Finite fields, volume 20 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, second edition, 1997. With a foreword by P. M. Cohn.
13. S. Lovett. Pseudorandom generators for low degree polynomials, 2007. Manuscript.
14. M. Luby, B. Velickovic, and A. Wigderson. Deterministic approximate counting of depth-2 circuits. In Proceedings of the 2nd Israeli Symposium on Theoretical Computer Science (ISTCS), pages 18-24, 1993.
15. J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications. In Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing, pages 213-223, 1990.
16. A. Samorodnitsky. Low-degree tests at large distances. In Proceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, CA USA, 2007.
17. A. Samorodnitsky and L. Trevisan. Gowers uniformity, influence of variables, and PCPs. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, USA, pages 11-20, 2006.
18. V. Shoup. New algorithms for finding irreducible polynomials over finite fields. Math. Comp., 54(189):435-447, 1990.
19. E. Viola. New correlation bounds for gf(2) polynomials using gowers uniformity. Electronic Colloquium on Computational Complexity, Technical Report TR06-097, 2006. http://www.eece.uni-trier.de/eccc.
20. E. Viola. Pseudorandom bits for constant-depth circuits with few arbitrary symmetric gates. SIAM Journal on Computing, 36(5):1387-1403, 2007.
21. E. Viola and A. Wigderson. Norms, xor lemmas, and lower bounds for GF(2) polynomials and multiparty protocols. In Proceedings of the 22nd Annual Conference on Computational Complexity. IEEE, June 13-16 2007.