Lower bounds on matrix rigidity via a quantum argument

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

Volumn 4051 LNCS, Issue , 2006, Pages 62-71

  De Wolf, Ronald ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER PROGRAMMING; COMPUTER SCIENCE; DIGITAL ARITHMETIC;

ARITHMETIC CIRCUITS; COMMUNICATION COMPLEXITY; LOWER BOUNDS; MATRIX RIGIDITY; QUANTUM COMPUTING;

QUANTUM THEORY;

EID: 33746360271     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11786986_7     Document Type: Conference Paper

References (24)

1. Valiant, L.: Graph-theoretic arguments in low-level complexity. In: Proceedings of 6th MFCS, Volume 53 of Lecture Notes in Computer Science., Springer (1977) 162-176
2. Alon, N.: On the rigidity of an Hadamard matrix. Manuscript. His proof may be found in [24, Section 15.1.2] (1990)
3. Lokam, S.: Spectral methods for matrix rigidity with applications to size-depth trade-offs and communication complexity. Journal of Computer and Systems Sciences 63(3) (2001) 449-473 Earlier version in FOGS'95.
4. Kashin, B., Razborov, A.: Improved lower bounds on the rigidity of Hadamard matrices. Matematicheskie Zametki 63(4) (1998) 535-540 In Russian. English translation available at Razborov's homepage.
5. Friedman, J.: A note on matrix rigidity. Combinatorica 13(2) (1993) 235-239
6. Shokrollahi, M.A., Spielman, D., Stemann, V.: A remark on matrix rigidity. Information Processing Letters 64(6) (1997) 283-285
7. Lokam, S.: On the rigidity of Vandermonde matrices. Theoretical Computer Science 237(1-2) (2000) 477-483
8. Lokam, S.: A quadratic lower bound on rigidity. (April 2005) Manuscript.
9. Lickteig, T.: Ein elementarer Beweis für eine geometrische Gradschanke für die Zahl der Operationen bei der Berechnung von Polynomen. Master's thesis, Diplomarbeit, Univ. Konstanz (1980)
10. Bürgisser, P., Clausen, M., Shokrollahi, M.A.: Algebraic Complexity Theory. Volume 315 of Grundlehren der mathematischen Wissenschaften. Springer (1997)
11. Nayak, A.: Optimal lower bounds for quantum automata and random access codes. In: Proceedings of 40th IEEE FOCS. (1999) 369-376 quant-ph/9904093.
12. Cleve, R., Dam, W. van, Nielsen, M., Tapp, A.: Quantum entanglement and the communication complexity of the inner product function. In: Proceedings of 1st NASA QCQC conference. Volume 1509 of Lecture Notes in Computer Science., Springer (1998) 61-74 quant-ph/9708019.
13. Kerenidis, I., Wolf, R. de: Exponential lower bound for 2-query locally decodable codes via a quantum argument. In: Proceedings of 35th ACM STOC. (2003) 106-115 quant-ph/0208062.
14. Wehner, S., Wolf, R. de: Improved lower bounds for locally decodable codes and private information retrieval. In: Proceedings of 32nd ICALP. Volume 3580 of Lecture Notes in Computer Science. (2005) 1424-1436 quant-ph/0403140.
15. Aharoriov, D., Regev, O.: A lattice problem in quantum NP. In: Proceedings of 44th IEEE FOCS. (2003) 210-219 quant-ph/0307220.
16. Aliaronov, D., Regev, O.: Lattice problems in NP∩coNP. In: Proceedings of 45th IEEE FOCS. (2004) 362-371
17. Aaronson, S.: Lower boundss for local search by quantum arguments. In: Proceedings of 35th ACM STOC, (2003) 465-474 quant-ph/0307149.
18. Aaronson, S.: Quantum computing, postselection, and probabilistic polynomial-time. quant-ph/041.2187 (23 Dec 2004.)
19. Laplante, S., Lee, T., Szegedy, M.: The quantum adversary method and classical formula size lower bounds. In: Proceedings of 20th IEEE Conference on Computational Complexity. (2005) quant-ph/0501057.
20. Kerenidis, I.: Quantum multiparty communication complexity and circuit lower bounds (Apr 12, 2005) quant-pli/0504087.
21. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)
22. Midrijanis, G.: Three lines proof of the lower bound for the matrix rigidity. cs.CC/0506081 (20 Jun 2005)
23. Alon, N., Spencer, J.H.: The Probabilistic Method, second edn. Wiley-Interscionce (2000)
24. Jukna, S.: Extremal Combinatorics. EATCS Series. Springer (2001)