메뉴 건너뛰기




Volumn , Issue , 2004, Pages 633-641

Multi-linear formulas for permanent and determinant are of super-Polynomial size

Author keywords

Algebraic complexity; Arithmetic formulas; Circuit complexity; Computational complexity; Lower bounds

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; POLYNOMIALS; PROBABILITY;

EID: 4544258177     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1007352.1007353     Document Type: Conference Paper
Times cited : (43)

References (17)
  • 1
    • 4544369758 scopus 로고    scopus 로고
    • Multilinear Formulas and Skepticism of Quantum Computing
    • S. Aaronson. Multilinear Formulas and Skepticism of Quantum Computing. STOC 2004
    • STOC 2004
    • Aaronson, S.1
  • 4
    • 0001567736 scopus 로고
    • Feasible arithmetic computations: Valiant's hypothesis
    • J. von zur Gathen. Feasible Arithmetic Computations: Valiant's Hypothesis. J. Symbolic Computation 4(2): 137-172 (1987)
    • (1987) J. Symbolic Computation , vol.4 , Issue.2 , pp. 137-172
    • Von Zur Gathen, J.1
  • 6
    • 0031639854 scopus 로고    scopus 로고
    • An exponential lower bound for depth 3 arithmetic circuits
    • D. Grigoriev, M. Karpinski. An Exponential Lower Bound for Depth 3 Arithmetic Circuits. STOC 1998: 577-582
    • STOC 1998 , pp. 577-582
    • Grigoriev, D.1    Karpinski, M.2
  • 7
    • 0033699197 scopus 로고    scopus 로고
    • Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields
    • preliminary version in FOCS 1998
    • D. Grigoriev, A. A. Razborov. Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields. Applicable Algebra in Engineering, Communication and Computing 10(6): 465-487 (2000) (preliminary version in FOCS 1998)
    • (2000) Applicable Algebra in Engineering, Communication and Computing , vol.10 , Issue.6 , pp. 465-487
    • Grigoriev, D.1    Razborov, A.A.2
  • 8
    • 0038107689 scopus 로고    scopus 로고
    • Derandomizing polynomial identity tests means proving circuit lower bounds
    • R. Impagliazzo, V. Kabanets. Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds. STOC 2003: 355-364
    • STOC 2003 , pp. 355-364
    • Impagliazzo, R.1    Kabanets, V.2
  • 9
    • 4544234244 scopus 로고
    • The formula size of the determinant
    • A. Kalorkoti. The Formula Size of the Determinant. SIAM Journal of Computing 14: 678-687 (1995)
    • (1995) SIAM Journal of Computing , vol.14 , pp. 678-687
    • Kalorkoti, A.1
  • 10
    • 85000547940 scopus 로고    scopus 로고
    • Lower bounds for non-Commutative computation
    • N. Nisan. Lower Bounds for Non-Commutative Computation. STOC 1991: 410-418
    • STOC 1991 , pp. 410-418
    • Nisan, N.1
  • 11
    • 0039648502 scopus 로고    scopus 로고
    • Lower bounds on arithmetic Circuits via partial derivatives
    • preliminary version in FOCS 1995
    • N. Nisan, A. Wigderson. Lower Bounds on Arithmetic Circuits Via Partial Derivatives. Computational Complexity 6(3): 217-234 (1996) (preliminary version in FOCS 1995)
    • (1996) Computational Complexity , vol.6 , Issue.3 , pp. 217-234
    • Nisan, A.1    Wigderson, N.2
  • 12
    • 4944248533 scopus 로고    scopus 로고
    • Deterministic polynomial identity testing in non commutative models
    • to appear
    • R. Raz, A. Shpilka. Deterministic Polynomial Identity Testing in Non Commutative Models. Conference on Computational Complexity 2004 (to appear)
    • (2004) Conference on Computational Complexity
    • Raz, A.1    Shpilka, R.2
  • 13
    • 0039270929 scopus 로고
    • A lower bound on the number of additions in monotone computations
    • C. P. Schnorr. A Lower Bound on the Number of Additions in Monotone Computations. Theoretical Computer Science 2(3): 305-315 (1976)
    • (1976) Theoretical Computer Science , vol.2 , Issue.3 , pp. 305-315
    • Schnorr, C.P.1
  • 14
  • 15
    • 0035729224 scopus 로고    scopus 로고
    • Depth-3 arithmetic aircuits over fields of characteristic zero
    • preliminary version in Conference on Computational Complexity 1999
    • A. Shpilka, A. Wigderson. Depth-3 Arithmetic Circuits Over Fields of Characteristic Zero. Computational Complexity 10(1): 1-27 (2001) (preliminary version in Conference on Computational Complexity 1999)
    • (2001) Computational Complexity , vol.10 , Issue.1 , pp. 1-27
    • Shpilka, A.1    Wigderson, A.2
  • 16
    • 85006998002 scopus 로고
    • Negation can be exponentially powerful
    • L. G. Valiant. Negation can be Exponentially Powerful. Theoretical Computer Science 12: 303-314 (1980)
    • (1980) Theoretical Computer Science , vol.12 , pp. 303-314
    • Valiant, L.G.1
  • 17
    • 0003370550 scopus 로고
    • Why is boolean complexity theory difficult?
    • (M. S. Paterson, ed.) Lond. Math. Soc. Lecture Note Ser. , Cambridge Univ. Press
    • L. G. Valiant. Why is Boolean Complexity Theory Difficult? In Boolean Function Complexity (M. S. Paterson, ed.) Lond. Math. Soc. Lecture Note Ser. Vol. 169, Cambridge Univ. Press 84-94 (1992)
    • (1992) Boolean Function Complexity , vol.169 , pp. 84-94
    • Valiant, L.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.