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Volumn 15, Issue 2, 2006, Pages 163-196

The quantum adversary method and classical formula size lower bounds

Author keywords

Adversary method; Communication complexity; Formula size; Lower bounds; Quantum computing

Indexed keywords


EID: 33745312939     PISSN: 10163328     EISSN: 14208954     Source Type: Journal    
DOI: 10.1007/s00037-006-0212-7     Document Type: Conference Paper
Times cited : (33)

References (39)
  • 2
    • 4243159779 scopus 로고    scopus 로고
    • Quantum lower bounds for the collision and the element distinctness problems
    • S. AARONSON & Y. SHI (2004). Quantum lower bounds for the collision and the element distinctness problems. J. ACM 51, 595-605.
    • (2004) J. ACM , vol.51 , pp. 595-605
    • Aaronson, S.1    Shi, Y.2
  • 3
    • 0042418642 scopus 로고    scopus 로고
    • Quantum lower bounds by quantum arguments
    • A. AMBAINIS (2002). Quantum lower bounds by quantum arguments. J. Comput. System Sci. 64, 750-767.
    • (2002) J. Comput. System Sci. , vol.64 , pp. 750-767
    • Ambainis, A.1
  • 5
    • 0346084217 scopus 로고
    • On a method for obtaining more than quadratic effective lower bounds for the complexity of ∏-schemes
    • A. E. ANDREEV (1987). On a method for obtaining more than quadratic effective lower bounds for the complexity of ∏-schemes. Moscow Univ. Math. Bull. 42, 63-65.
    • (1987) Moscow Univ. Math. Bull. , vol.42 , pp. 63-65
    • Andreev, A.E.1
  • 9
    • 0039467239 scopus 로고
    • Amplification of probabilistic Boolean formulas
    • R. BOPPANA (1989). Amplification of probabilistic Boolean formulas. Adv. Comput. Res. 5, 27-45.
    • (1989) Adv. Comput. Res. , vol.5 , pp. 27-45
    • Boppana, R.1
  • 11
    • 0037048579 scopus 로고    scopus 로고
    • Complexity measures and decision tree complexity: A survey
    • H. BUHRMAN & R. DE WOLF (2002). Complexity measures and decision tree complexity: A survey. Theoret. Comput. Sci. 288, 21-43.
    • (2002) Theoret. Comput. Sci. , vol.288 , pp. 21-43
    • Buhrman, H.1    De Wolf, R.2
  • 12
    • 5544275298 scopus 로고    scopus 로고
    • Amplification by read-once formulas
    • M. DUBINER & U. ZWICK (1997). Amplification by read-once formulas. SIAM J. Comput. 26, 15-38.
    • (1997) SIAM J. Comput. , vol.26 , pp. 15-38
    • Dubiner, M.1    Zwick, U.2
  • 13
    • 0004003953 scopus 로고    scopus 로고
    • The shrinkage exponent is 2
    • J. HÅSTAD (1998). The shrinkage exponent is 2. SIAM J. Comput. 27, 48-64.
    • (1998) SIAM J. Comput. , vol.27 , pp. 48-64
    • Håstad, J.1
  • 18
    • 4544225791 scopus 로고    scopus 로고
    • Exponential lower bound for 2-query locally decodable codes via a quantum argument
    • I. KERENIDIS & R. DE WOLF (2004). Exponential lower bound for 2-query locally decodable codes via a quantum argument. J. Comput. System Sci. 69, 395-420.
    • (2004) J. Comput. System Sci. , vol.69 , pp. 395-420
    • Kerenidis, I.1    De Wolf, R.2
  • 19
    • 5544274004 scopus 로고
    • Complexity of the realization of a linear function in the case of ∏-circuits
    • V. M. KHRAPCHENKO (1971). Complexity of the realization of a linear function in the case of ∏-circuits. Math. Notes 9, 21-23.
    • (1971) Math. Notes , vol.9 , pp. 21-23
    • Khrapchenko, V.M.1
  • 20
    • 27644526983 scopus 로고    scopus 로고
    • One-way communication complexity and the Nečiporuk lower bound on formula size
    • cs.CC arXiv.
    • H. KLAUCK (2004). One-way communication complexity and the Nečiporuk lower bound on formula size. Technical Report 0111062, cs.CC arXiv. URL http://www.arxiv.org/abs/cs.CC/0111062.
    • (2004) Technical Report 0111062
    • Klauck, H.1
  • 21
    • 0027649264 scopus 로고
    • Improvements on Khrapchenko's theorem
    • E. KOUTSOUPIAS (1993). Improvements on Khrapchenko's theorem. Theoret. Comput. Sci. 116, 399-403.
    • (1993) Theoret. Comput. Sci. , vol.116 , pp. 399-403
    • Koutsoupias, E.1
  • 23
    • 4944231386 scopus 로고    scopus 로고
    • Lower bounds for randomized and quantum query complexity using Kolmogorov arguments
    • IEEE
    • S. LAPLANTE & F. MAGNIEZ (2004). Lower bounds for randomized and quantum query complexity using Kolmogorov arguments. In Proc. 19th IEEE Conference on Computational Complexity, IEEE, 294-304.
    • (2004) Proc. 19th IEEE Conference on Computational Complexity , pp. 294-304
    • Laplante, S.1    Magniez, F.2
  • 26
    • 0141738444 scopus 로고    scopus 로고
    • On the noise sensitivity of monotone functions
    • E. MOSSELL & R. O'DONNELL (2003). On the noise sensitivity of monotone functions. Random Structures Algorithms 23, 333-350.
    • (2003) Random Structures Algorithms , vol.23 , pp. 333-350
    • Mossell, E.1    O'Donnell, R.2
  • 28
    • 0026389757 scopus 로고
    • CREW PRAMs and decision trees
    • N. NISAN (1991). CREW PRAMs and decision trees. SIAM J. Comput. 20, 999-1007.
    • (1991) SIAM J. Comput. , vol.20 , pp. 999-1007
    • Nisan, N.1
  • 29
    • 0000607672 scopus 로고
    • On the degree of Boolean functions as real polynomials
    • N. NISAN & M. SZEGEDY (1994). On the degree of Boolean functions as real polynomials. Comput. Complexity 4, 301-313.
    • (1994) Comput. Complexity , vol.4 , pp. 301-313
    • Nisan, N.1    Szegedy, M.2
  • 31
    • 0011933971 scopus 로고
    • Applications of matrix methods to the theory of lower bounds in computational complexity
    • A. RAZBOROV (1990). Applications of matrix methods to the theory of lower bounds in computational complexity. Combinatorica 10, 81-93.
    • (1990) Combinatorica , vol.10 , pp. 81-93
    • Razborov, A.1
  • 32
    • 0011958653 scopus 로고
    • On submodular complexity measures
    • M. Paterson (ed.), London Math. Soc. Lecture Note Ser. 169, Cambridge Univ. Press
    • A. RAZBOROV (1992). On submodular complexity measures. In Boolean Function Complexity, M. Paterson (ed.), London Math. Soc. Lecture Note Ser. 169, Cambridge Univ. Press, 76-83.
    • (1992) Boolean Function Complexity , pp. 76-83
    • Razborov, A.1
  • 33
    • 0020736827 scopus 로고
    • New lower bounds on the formula size of Boolean functions
    • U. SCHÜRFELD (1983). New lower bounds on the formula size of Boolean functions. Acta Inform. 19, 183-194.
    • (1983) Acta Inform. , vol.19 , pp. 183-194
    • Schürfeld, U.1
  • 36
    • 0004021233 scopus 로고
    • On time-hardware complexity tradeoffs for Boolean functions
    • Western Periodicals Company, North Hollywood
    • P. SPIRA (1971). On time-hardware complexity tradeoffs for Boolean functions. In Proc. 4th Hawaii Symposium on System Sciences, Western Periodicals Company, North Hollywood, 525-527.
    • (1971) Proc. 4th Hawaii Symposium on System Sciences , pp. 525-527
    • Spira, P.1
  • 37
    • 84861255164 scopus 로고    scopus 로고
    • 1.3) quantum algorithm for the triangle finding problem
    • Quant-ph/0310134
    • 1.3) quantum algorithm for the triangle finding problem. Technical report. Quant-ph/0310134.
    • (2003) Technical Report
    • Szegedy, M.1
  • 38
    • 0000378392 scopus 로고
    • Short monotone formulae for the majority function
    • L. G. VALIANT (1984). Short monotone formulae for the majority function. J. Algorithms 5, 363-366.
    • (1984) J. Algorithms , vol.5 , pp. 363-366
    • Valiant, L.G.1
  • 39
    • 18544371325 scopus 로고    scopus 로고
    • On the power of Ambainis's lower bounds
    • S. ZHANG (2005). On the power of Ambainis's lower bounds. Theoret. Comput. Sci. 339, 241-256.
    • (2005) Theoret. Comput. Sci. , vol.339 , pp. 241-256
    • Zhang, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.