Gowers uniformity, influence of variables, and PCPs

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn 2006, Issue , 2006, Pages 11-20

  Samorodnitsky, Alex ^a   Trevisan, Luca ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Influence of variables; Linearity test; Probabilistically checkable proofs

Indexed keywords

APPROXIMATION THEORY; BOOLEAN FUNCTIONS; COMPUTATION THEORY; ERROR CORRECTION; GRAPH THEORY; POLYNOMIALS; PROBABILITY;

INFLUENCE OF VARIABLES; LINEARITY TEST; PROBABILISTICALLY CHECKABLE PROOFS; RANDOM FUNCTION;

QUERY LANGUAGES;

EID: 33748120485     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132519     Document Type: Conference Paper

References (40)

1. Yonatan Aumann, Johan Håstad, Michael O. Rabin, and Madhu Sudan. Linear-consistency testing. Journal of Computer and System Sciences, 4(62):589-607, 2001.
2. Noga Alon, Tali Kaufman, Michael Krivelevich, Simon Litsyn, and Dana Ron. Testing low-degree polynomials over GF(2). In Proceedings of RANDOM-APPROX, pages 188-199, 2003.
3. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems. Journal of the ACM, 45(3):501-555, 1998.
4. Preliminary version in Proc. of FOCS'92.
5. Sanjeev Arora. How NP got a new definition: a survey of probabilistically checkable proofs. In Proceedings of the International Congress of Mathematicians, pages 637-648, 2002. Volume 3.
6. S. Arora and S. Safra. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM, 45(1):70-122, 1998.
7. Preliminary version in Proc. of FOCS'92.
8. M. Bellare, D. Coppersmith, J. Håstad, M. Kiwi, and M. Sudan. Linearity testing over characteristic two. IEEE Transactions on Information Theory, 42(6):1781-1795, 1996.
9. M. Bellare, O. Goldreich, and M. Sudan. Free bits, PCP's and non-approximability - towards tight results. SIAM Journal on Computing, 27(3):804-915, 1998.
10. Preliminary version in Proc. of FOCS'95.
11. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. Journal of Computer and System Sciences, 47(3):549-595, 1993.
12. Preliminary version in Proc. of STOC'90.
13. Shuchi Chawla, Robert Krauthgamer, Ravi Kumar, Yuval Rabani, and D.Sivakumar. On the hardness of approximating multicut and sparsest-cut. In Proceedings of the 20th IEEE Conference on Computational Complexity, 2005.
14. Irit Dinur and Shmuel Safra. On the hardness of approximating minimum vertex-cover. Annals of Mathematics, 162(1):439-486, 2005.
15. Lars Engebretsen and Jonas Holmerin. More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP. pages 194-205, 2005.
16. Uriel Feige. Approximation thresholds for combinatorial optimization problems. In Proceedings of the International Congress of Mathematicians, pages 649-658, 2002. Volume 3.
17. Timothy Gowers. A new proof of Szeméredi's theorem for progressions of length four. Geometric and Functional Analysis, 8(3):529-551, 1998.
18. Timothy Gowers. A new proof of Szeméredi's theorem. Geometric and Functional Analysis, 11(3):465-588, 2001.
19. Ben Green and Terence Tao. The primes contain arbitrarily long arithmetic progressions. To appear in Annals of Mathematics. math.NT/0404188, 2004.
20. 3 norm. math.NT/0503014, 2005.
21. 1-ε. Acta Mathematica, 182:105-142, 1999.
22. Johan Håstad. Some optimal inapproximability results. Journal of the ACM, 48(4):798-859, 2001.
23. Gustav Hast. Approximating Max kCSP outperforming a random assignment with almost a linear factor, pages 956-968, 2005.
24. Bernard Host and Bryna Kra. Nonconventional ergodic averages and nilmanifolds. Annals of Mathematics, 161(1):397-488, 2005.
25. Johan Håstad and Avi Wigderson. Simple analysis of graph tests for linearity and PCP. Random Structures and Algorithms, 22(2): 139-160, 2003.
26. Charanjit S. Jutla, Anindya C. Patthak, Atri Rudra, and David Zuckerman. Testing low-degree polynomials over prime fields. In Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, pages 423-432, 2004.
27. J. Kahn, G. Kalai, and N. Linial The influence of variables on boolean functions. In Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, pp. 68-80, 1988.
28. Subhash Knot. On the power of unique 2-prover 1-round games. In Proceedings of the 34th ACM Symposium on Theory of Computing, pages 767-775, 2002.
29. Subhash Khot, Guy Kindler, Elchanan Mossel, and Ryan O'Donnell. Optimal inapproximability results for MAX-CUT and other two-variable CSPs? In Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, pages 146-154, 2004.
30. Subhash Knot and Oded Regev. Vertex cover might be hard to approximate to within 2 - ε. In Proceedings of the 18th IEEE Conference on Computational Complexity, 2003.
31. Tali Kaufman and Dana Ron. Testing polynomials over general fields. In Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, pages 413-422, 2004.
32. Bryna Kra. The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view. Bulletin of the AMS. To appear.
33. 1. In Proceedings of the 46th IEEE Symposium on Foundations of Computer Science, pages 53-62, 2005.
34. Alex Samorodnitsky. Hypergraph linearity and quadraticity tests for boolean functions. Manuscript, 2005.
35. Alex Samorodnitsky and Luca Trevisan. A PCP characterization of NP with optimal amortized query complexity. In Proceedings of the 32nd ACM Symposium on Theory of Computing, pages 191-199, 2000.
36. Luca Trevisan. Parallel approximation algorithms by positive linear programming. Algorithmica, 21(1):72-88, 1998.
37. Preliminary version in Proc. of ESA '96.
38. Luca Trevisan. Non-approximability results for optimization problems on bounded degree instances. In Proceedings of the 33rd ACM Symposium on Theory of Computing, pages 453-461, 2001.
39. Luca Trevisan. Inapproximability of combinatorial optimization problems. Technical Report TR04-065, Electronic Colloquium on Computational Complexity, 2004.
40. Vijay Vazirani. Approximation Algorithms. Springer, 2001.