The quantum adversary method and classical formula size lower bounds

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2005, Pages 76-90

  Laplante, Sophie ^a   Lee, Troy ^b   Szegedy, Mario ^c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

^c RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMMUNICATION COMPLEXITY; QUANTUM ADVERSARY METHOD; QUANTUM QUERY COMPLEXITY;

COMPUTATIONAL COMPLEXITY; FUNCTIONS; MATRIX ALGEBRA; PROBABILISTIC LOGICS; RECURSIVE FUNCTIONS;

QUANTUM THEORY;

EID: 27644557352     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (39)

1. [Aar04] S. Aaronson. Lower bounds for local search by quantum arguments. In Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, pages 465-474, 2004.
2. [Amb02] A. Ambainis. Quantum lower bounds by quantum arguments. Journal of Computer and System Sciences, 64:750-767, 2002.
3. [Amb03] A. Ambainis. Polynomial degree vs. quantum query complexity. In Proceedings of 44th IEEE Symposium on Foundations of Computer Science, pages 230-239, 2003.
4. [And87] A. E. Andreev. On a method for obtaining more than quadratic effective lower bounds for the complexity of II-schemes. Moscow Univ. Math. Bull., 42(1):63-66, 1987.
5. [AS04] S. Aaronson and Y. Shi. Quantum lower bounds for the collision and the element distinctness problems. Journal of the ACM, 51(4):595-605, 2004.
6. [BBBV97] C.H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing. SIAM Journal on Computing, 26:1510-1523, 1997.
7. +01] R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials. Journal of the ACM, 48(4):778-797, 2001.
8. [BHT97] G. Brassard, P. Høyer, and A. Tapp. Quantum algorithm for the collision problem. ACM SIGACT News (Cryptology column), 28:14-19, 1997.
9. [Bop89] R. Boppana. Amplification of probabilistic boolean formulas. Advances in Computing Research, 5(4):27-45, 1989.
10. [BSS03] H. Barnum, M. Saks, and M. Szegedy. Quantum decision trees and semidefinite programming. In Proceedings of the 18th IEEE Conference on Computational Complexity, pages 179-193, 2003.
11. [BW02] H. Buhrman and R. de Wolf. Complexity measures and decision tree complexity: A survey. Theoretical Computer Science, 288:21-43, 2002.
12. [DZ97] M. Dubiner and U. Zwick. Amplification by read-once formulas. SIAM J. Comput., 26(1):15-38, 1997.
13. [Gro96] L. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of 28th ACM Symposium on Theory of Computing, pages 212-219, 1996.
14. [Hås98] J. Håstad. The shrinkage exponent of de Morgan formulae is 2. SIAM Journal on Computing, 2719(1):48-64, 1998.
15. [HJ99] R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, 1999.
16. [JKS03] T. Jayram, R. Kumar, and D. Sivakumar. Two applications of information complexity. In Proceedings of the 35th ACM Symposium on the Theory of Computing, pages 673-682, 2003.
17. [Khr71] V.M. Khrapchenko. Complexity of the realization of a linear function in the case of II-circuits. Math. Notes Acad. Sciences, 9:21-23, 1971.
18. [Kla04] H. Klauck. One-way communication complexity and the Nediporuk lower bound on formula size. Technical Report 0111062, cs.CC arXiv, 2004.
19. [Kou93] E. Koutsoupias. Improvements on Khrapchenko's theorem. Theoretical Computer Science, 116(2):399-403, 1993.
20. [KW88] M. Karchmer and A. Wigderson. Monotone connectivity circuits require super-logarithmic depth. In Proceedings of the 20th STOC, pages 539-550, 1988.
21. [KW03] I. Kerenidis and R. de Wolf. Exponential lower bound for 2-query locally decodable codes via a quantum argument. In Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pages 106-115, 2003.
22. [KKN95] M. Karchmer, E. Kushilevitz and N. Nisan. Fractional Covers and Communication Complexity. SIAM Journal on Discrete Mathematics, 8(1):76-92, 1995.
23. [LM04] S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using Kolmogorov arguments. In Proceedings of the Nineteenth Annual IEEE Conference on Computational Complexity, pages 294-304, 2004.
24. [LV97] M. Li and P. Vitányi. An introduction to Kolmogorov complexity and its applications. In Graduate Texts in Computer Science. Springer, 1997. Second edition.
25. [MO03] E. Mossell and R. O'Donnell. On the noise sensitivity of monotone functions. Random Structures and Algorithms, 23(3):333-350, 2003.
26. [NC00] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
27. [Nis91] N. Nisan. CREW PRAMs and decision trees. SIAM Journal on Computing, 20(6):999-1007, 1991.
28. [NS94] N. Nisan and M. Szegedy. On the degree of boolean functions as real polynomials. Computational Complexity, 4:301-313, 1994.
29. [O'D02] R. O'Donnell. Hardness amplification within NP. In Proceedings of the 34th ACM Symposium on the Theory of Computing, pages 751-760. ACM, 2002.
30. [Raz90] A. Razborov. Applications of matrix methods to the theory of lower bounds in computational complexity. Combinatorica, 10(1):81-93, 1990.
31. [Raz92] A. Razborov. On submodular complexity measures. In Boolean Function Complexity. London Math. Soc. Lecture Notes Series, 169, pages 76-83, 1992.
32. [Sch83] U. Schürfeld. New lower bounds on the formula size of Boolean functions. Acta Informatica, 19(2):183-194, 1983.
33. [Sha49] C.E. Shannon. The synthesis of two-terminal switching circuits. Bell System Technical Journal, 28(1):59-98, 1949.
34. [Spi71] P. Spira. On time-hardware complexity tradeoffs for Boolean functions. In Proceedings of the 4th Hawaii Symposium on System Sciences, pages 525-527. Western Periodicals Company, North Hollywood, 1971.
35. [ŠS04] R. Špalek and M. Szegedy. All quantum adversary methods are equivalent. Technical Report 0409116, quant-ph, 2004.
36. [SV01] P. Sen and S. Venkatesh. Lower bounds in the quantum cell probe model. In Proceedings of Intenational Colloquium on Automata, Languages and Programming (ICALP), pages 358-369, 2001.
37. 1.3) quantum algorithm for the triangle finding problem. Technical Report 0310134, quant-ph, 2003.
38. [Val84] L.G. Valiant. Short monotone formulae for the majority function. Journal of Algorithms, 5:363-366, 1984.
39. [Zha04] S. Zhang. On the power of Ambainis's lower bounds. In Proceedings of 31st International Colloquium on Automata, Languages and Programming, 2004. To appear. Also in quant-ph/0311060.