On the correlation between parity and modular polynomials

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

Volumn 4162 LNCS, Issue , 2006, Pages 387-398

  Gál, Anna ^a   Trifonov, Vladimir ^a  

^a University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SCIENCE; CORRELATION METHODS; LINEAR ALGEBRA; PROBLEM SOLVING;

GOLDMANN'S RESULT; MODULAR POLYNOMIALS; UPPER BOUNDS;

POLYNOMIALS;

EID: 33750083306     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11821069_34     Document Type: Conference Paper

References (26)

1. 1-formulae on finite structures. Ann. Pure Appl. Logic 24, 1983, 1-48.
2. [Al] E. Allender. A note on the power of threshold circuits. Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, 1989, 580-584.
3. m, Proceedings of the 16th Annual IEEE Conference on Computational Complexity, 2001, 184-187
4. 1. Journal of Computer and System Sciences 38 (1989), 150-164.
5. [BM] R. Beigel, A. Maciel. Upper and lower bounds for some depth-3 circuit classes, in Proceedings of the 30th Symposium on Foundations of Computer Science, 1989, 580-584.
6. [Bo05] J. Bourgain. Estimation of certain exponential sums arising in complexity theory, C.R. Acad. Sci. Paris Ser. I 340 (2005) pp. 627-631.
7. [CGT] J.-Y. Cai, F. Green, and T. Thierauf. On the correlation of symmetric functions. Mathematical Systems Theory 29 (1996), 245-258.
8. [FSS] M. Furst, J. Saxe, and M. Sipser. Parity, circuits, and the polynomial hierarchy. Mathematical Systems Theory 17, 1984, 13-27.
9. [Gr99] F. Green. Exponential sums and circuits with single threshold gate and mod-gates , Theory Computing Systems 32 (1999), 453-466.
10. [Gr02] F. Green. The Correlation between parity and quadratic polynomials mod 3, Proceedings of the 17th Annual IEEE Conference on Computational Complexity, 2002, 65-72.
11. [GRS] F. Green, A. Roy, H. Straubing. Bounds on an exponential sum arising in boolean circuit complexity, C.R. Acad. Sci. Paris Ser. I 340 (2005).
12. [Go] M. Goldmann. A note on the power of majority gates and modular gates, Information Processing Letters 53 (1995), 321-327
13. [Gro] V. Grolmusz. A weight-size tradeoff for circuits with mod m gates, in Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, 68-74.
14. m circuits, SIAM J. Comput., 29, No. 4, 2000, 1209-1222.
15. [HMPST] A. Hajnal, W. Maass, P. Pudlák, M. Szegedy, and G. Turán. Threshold Circuits of bounded depth, Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, 1987, 99-110
16. [HM] K. Hansen and P. Miltersen. Some meet-in-the-middle circuit lower bounds. in Proceedings of MFCS, 2004, 334-345.
17. [Ha] J. Håstad. Computational Limitations of Small-Depth Circuits. MIT Press, 1986.
18. [HG] J. Håstad and M. Goldmann. On the power of small depth threshold circuits. Computational Complexity 1(2), 1991, 113-129.
19. [KP] M. Krause, P. Pudlák. On the computational power of depth 2 circuits with threshold and modulo gates, in Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, 48-57.
20. [LN] R. Lidl and H. Niederreiter. Introduction to Finite Fields and Their Applications, Cambridge University Press.
21. ω(log n) Lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom. Information Processing Letters 45, 1993, 303-307.
22. [Sm] R. Smolensky. Algebraic methods in the theory of lower bounds for boolean circuit complexity, Proceedings of the 19th Annual ACM Symposium on Theory of Computi ng, 1987, 77-82
23. [Sz] G. Szegö. Orthogonal Polynomials. American Mathematical Society, 1939.
24. [Yao85] A. Yao. Separating the polynomial hierarchy by oracles. Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, 1985, 1-10.
25. [Yao90] A. Yao. On ACC and threshold circuits. Proceedings of the 31th Annual IEEE Symposium on Foundations of Computer Science, 1990, 619-627.
26. n). Ann. Univ. Mariae Curie Sklodowska, A10 (1956), pp. 37-47.