On the fourier tails of bounded functions over the discrete cube

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn 2006, Issue , 2006, Pages 437-446

  Dinur, Irit ^a   Friedgut, Ehud ^a   Kindler, Guy ^b   O'Donnell, Ryan ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b MICROSOFT RESEARCH   (United States)

Author keywords

Boolean functions; Fourier analysis; Symmetry breaking

Indexed keywords

BOOLEAN FUNCTIONS; CHEBYSHEV APPROXIMATION; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; POLYNOMIALS; THEOREM PROVING;

BOUNDED FUNCTIONS; FOURIER ANALYSIS; HARDNESS OF APPROXIMATION PROBLEMS; SYMMETRY BREAKING;

NUMERICAL METHODS;

EID: 33748109882     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132580     Document Type: Conference Paper

References (33)

1. N. Alon, I. Dinur, E. Friedgut, and B. Sudakov. Graph products, fourier analysis and spectral techniques. To appear in GAFA, 2003.
2. S. Arora, E. Berger, E. Hazan, G. Kindler, and S. Safra. On non-approximability for quadratic programs. In Proc. 46th Ann. FOCS, 2005.
3. M. Ben-Or and N. Linial. Collective coin flipping. In S. Micali, editor, Randomness and Computation, Academic Press, New York, 1990.
4. J. Bourgain. On the distribution of the Fourier spectrum of boolean functions. Israel J. of Math., 131:269-276, 2002.
5. S. Chawla, R. Krauthgamer, R. Kumar, Y. Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. In Proc. 20th Ann. CCC, 2005.
6. I. Dinur. The PCP theorem by gap amplification. Accepted STOC, 2006.
7. I. Dinur, E. Mossel, and O. Regev. Conditional hardness for approximate coloring. Accepted STOC, 2006.
8. I. Dinur, E. Friedgut, G. Kindler, and R. O'Donnell. On the Fourier tails of bounded functions over the discrete cube. Israel Journal of Mathematics, to appear, 2006.
9. I. Dinur, V. Guruswami, S. Khot, and O. Regev. A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover. In Proc. of the 35th Ann. STOC, 2003.
10. I. Dinur and S. Safra. On the hardness of approximating minimum vertex cover. Annals of Mathematics, 162(1), 2005.
11. E. Friedgut and J. Bourgain. Sharp thresholds of graph properties, and the k-sat problem. JAMS: Journal of the American Mathematical Society, 12, 1999.
12. E. Friedgut. Boolean functions with low average sensitivity depend on few coordinates. Combinatorica, 18(1):474-483, 1998.
13. E. Friedgut and G. Kalai. Every monotone graph property has a sharp threshold. Proc. Amer. Math. Soc., 124:2993-3002, 1996.
14. E. Friedgut, G. Kalai, and A. Naor. Boolean functions whose Fourier transform is concentrated on the first two levels. Advances in Applied Mathematics, 29(3):427-437, 2002.
15. S. Janson. Gaussian Hubert Spaces. Cambridge University Press, 1997.
16. J. Kahn, G. Kalai, and N. Linial. The influence of variables on Boolean functions. In Proc. 29th Ann. FOCS, 1988.
17. S. Khot and O. Regev. Vertex cover might be hard to approximate to within /spl epsi/. In Annual IEEE Conference on Computational Complexity (formerly Annual Conference on Structure in Complexity Theory), volume 18, 2003.
18. S. Khot. On the power of unique 2-prover 1-round games. In Proc. 34th Ann. STOC, 2002.
19. S. Khot, G. Kindler, E. Mossel, and R. O'Donnell. Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? In Proc. 45th IEEE Symp. on Foundations of Computer Science, 2004.
20. S. Khot and A. Naor. Nonembeddability theorems via fourier analysis, Oct. 26 2005. Comment: With an appendix on quantitative estimates in Bourgain's noise sensitivity theorem. To appear in Mathematiche Annalen. An extended abstract appeared in FOCS 2005.
21. S. Khot and R. O'Donnell. Lower bounds for Grothendieck problems. Manuscript.
22. S. Khot and N. Vishnoi. The Unique Games Conjecture, integrality gap for cut problems and embeddability of negative type metrics into 11. In Proc. 46rd Ann. IEEE Foundations of Computer Science, 2005.
23. G. Kindler and S. Safra. Noise-resistant boolean functions are juntas, manuscript.
24. A. Klivans, R. O'Donnell, and R. Servedio. Learning intersections and thresholds of halfspaces. JCSS: Journal of Computer and System Sciences, 68, 2004.
25. 1. To appear in SODA 2006.
26. M. Ledoux and M. Talagrand. Probability in Banach Spaces. Springer, 1991.
27. B. Mossel, R. O'Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: invariance and optimality. In Proc. 46th Ann. FOCS, 2005.
28. R. O'Donnell. Hardness amplification within NP, In STOC, pages 751-760, 2002.
29. R. O'Donnell and R. Servedio. Learning monotone functions in polynomial. Manuscript.
30. K. Oleszkiewicz. On the non-symmetric Khinchine-Kahane inequality. Private communication, 2002.
31. R. Raz. Fourier analysis for probabilistic communication complexity. Computational Complexity, 5(3/4):205-221, 1995.
32. T. J. Rivlin. Chebyshev Polynomials. John Wiley & Sons, New York, second edition, 1990.
33. M. Talagrand. On Russo's approximate 0-1 law. The Annals of Probability, 22(3):1576-1587, 1994.