Dual lower bounds for approximate degree and Markov-Bernstein inequalities

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

Volumn 7965 LNCS, Issue PART 1, 2013, Pages 303-314

  Bun, Mark ^a   Thaler, Justin ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AND-OR TREE; COMPLEXITY MEASURES; DUAL SOLUTIONS; LINEAR PROGRAMS; LOWER BOUNDS; MINIMUM DEGREE; SYMMETRIC BOOLEAN FUNCTIONS; THEORETICAL COMPUTER SCIENCE;

BOOLEAN FUNCTIONS; LINEAR PROGRAMMING;

AUTOMATA THEORY;

EID: 84880304959     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-39206-1_26     Document Type: Conference Paper

References (35)

1. Aaronson, S.: The polynomial method in quantum and classical computing. In: Proc. of Foundations of Computer Science (FOCS), p. 3 (2008), Slides available at http://www.scottaaronson.com/talks/polymeth.ppt
2. Aaronson, S., Shi, Y.: Quantum lower bounds for the collision and the element distinctness problems. Journal of the ACM 51(4), 595-605 (2004)
3. Ambainis, A.: Polynomial degree and lower bounds in quantum complexity: Collision and element distinctness with small range. Theory of Computing 1(1), 37-46 (2005)
4. Chattopadhyay, A., Ada, A.: Multiparty communication complexity of disjointness. Electronic Colloquium on Computational Complexity (ECCC) 15(002) (2008)
5. Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bound by polynomials. Journal of the ACM 48(4), 778-797 (2001)
6. Beame, P., Machmouchi, W.: The quantum query complexity of AC0 . Quantum Information & Computation 12(7-8), 670-676 (2012)
7. Beigel, R.: The polynomial method in circuit complexity. In: Proc. of the Conference on Structure in Complexity Theory, pp. 82-95 (1993)
8. Beigel, R.: Perceptrons, PP, and the polynomial hierarchy. In: Computational Complexity, vol. 4, pp. 339-349 (1994)
9. Bernstein, S.N.: On the V. A. Markov theorem. Trudy Leningr. Industr. In-ta, no 5, razdel fiz-matem nauk, 1 (1938)
10. Buhrman, H., Vereshchagin, N.K., de Wolf, R.: On computation and communication with small bias. In: Proc. of the Conference on Computational Complexity, pp. 24-32 (2007)
11. Høyer, P., Mosca, M., de Wolf, R.: Quantum search on bounded-error inputs. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 291-299. Springer, Heidelberg (2003)
12. Gavinsky, D., Sherstov, A.A.: A separation of NP and coNP in multiparty communication complexity. Theory of Computing 6(1), 227-245 (2010)
13. Kalai, A., Klivans, A.R., Mansour, Y., Servedio, R.A.: Agnostically learning halfspaces. SIAM Journal on Computing 37(6), 1777-1805 (2008)
14. Klauck, H., Špalek, R., de Wolf, R.: Quantum and classical strong direct product theorems and optimal time-space tradeoffs. SIAM Journal on Computing 36(5), 1472-1493 (2007)
15. Õ(n1/3). J. of Comput. and System Sci. 68(2), 303-318 (2004)
16. Klivans, A.R., Sherstov, A.A.: Lower bounds for agnostic learning via approximate rank. Computational Complexity 19(4), 581-604 (2010)
17. Lee, T., Shraibman, A.: Disjointness is hard in the multi-party number-on-the-forehead model. In: Proc. of the Conference on Computational Complexity, pp. 81-91 (2008)
18. Markov, V.: On functions which deviate least from zero in a given interval, St. Petersburg (1892) (Russian)
19. Minsky, M.L., Papert, S.A.: Perceptions: An Introduction to Computational Geometry. MIT Press, Cambridge (1969)
20. Open problems in analysis of Boolean functions. Compiled for the Simons Symposium. CoRR, abs/1204.6447, February 5-11 (2012)
21. Nisan, N., Szegedy, M.: On the degree of boolean functions as real polynomials. Computational Complexity 4, 301-313 (1994)
22. Paturi, R.: On the degree of polynomials that approximate symmetric Boolean functions (Preliminary Version). In: Proc. of the Symp. on Theory of Computing (STOC), pp. 468-474 (1992)
23. Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons, New York (1986)
24. Sherstov, A.A.: Approximate inclusion-exclusion for arbitrary symmetric functions. Computational Complexity 18(2), 219-247 (2009)
25. Sherstov, A.A.: Approximating the AND-OR tree. Electronic Colloquium on Computational Complexity (ECCC) 20(023) (2013)
26. Sherstov, A.A.: Communication lower bounds using dual polynomials. Bulletin of the EATCS 95, 59-93 (2008)
27. Sherstov, A.A.: The pattern matrix method. SIAM J. Comput. 40(6), 1969-2000 (2011)
28. Sherstov, A.A.: Making polynomials robust to noise. In: Proceedings of Symp. Theory of Computing, pp. 747-758 (2012)
29. 0 from depth-2 majority circuits. SIAM Journal on Computing 28(6), 2113-2129 (2009)
30. Sherstov, A.A.: The intersection of two halfspaces has high threshold degree. In: Proc. of Foundations of Computer Science (FOCS), pp. 343-362 (2009);
31. To appear in SIAM J. Comput. (special issue for FOCS 2009)
32. Sherstov, A.A.: The multiparty communication complexity of set disjointness. In: Proceedings of Symp. Theory of Computing, pp. 525-548 (2012)
33. Shi, Y.: Approximating linear restrictions of Boolean functions. Manuscript (2002), http://web.eecs.umich.edu/~shiyy/mypapers/linear02-j.ps
34. Shi, Y., Zhu, Y.: Quantum communication complexity of block-composed functions. Quantum Information & Computation 9(5), 444-460 (2009)
35. Špalek, R.: A dual polynomial for OR. Manuscript (2008), http://arxiv.org/abs/0803.4516