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Abstract: An arithmetic formula is multi-linear if the polynomial computed by each of its sub-formulas is multi-linear. We prove that any multi-linear arithmetic formula for the permanent or the determinant of an n n matrix is of size super-polynomial in n. (Update)
Cited by: More
Multilinear Formulas and Skepticism of Quantum Computing - Aaronson (2004) (Correct)
Multilinear-NC1 ≠ Multilinear-NC2 - Raz (Correct)
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0.6: Deterministic Polynomial Identity Testing in Non Commutative.. - Raz, Shpilka (2004) (Correct)
0.5: On the Complexity of Matrix Product - Raz (2002) (Correct)
0.3: Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
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0.2: On Interpolation and Automatization for Frege Systems - Bonet, Pitassi, Raz (2000) (Correct)
0.2: Multilinearity Can Be Exponentially Restrictive - Sengupta, Venkateswaran (1994) (Correct)
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BibTeX entry: (Update)
R. Raz. Multi-linear formulas for permanent and determinant are of super-polynomial size, submitted, 2003. ECCC TR03-067. http://citeseer.ist.psu.edu/raz03multilinear.html More
@misc{ raz03multilinear,
author = "R. Raz",
title = "Multi-linear formulas for permanent and determinant are of super-polynomial
size",
text = "R. Raz. Multi-linear formulas for permanent and determinant are of super-polynomial
size, submitted, 2003. ECCC TR03-067.",
year = "2003",
url = "citeseer.ist.psu.edu/raz03multilinear.html" }
Citations (may not include all citations):58 Algebraic Complexity Theory (context) - Burgisser, Clausen et al. - 1997
22 Lower Bounds for Non-Commutative Computation (context) - Nisan - 1991
16 Algebraic Complexity Theory (context) - Gathen - 1988
14 An Exponential Lower Bound for Depth 3 Arithmetic Circuits - Grigoriev, Karpinski - 1998
14 Exponential Lower Bounds for Depth 3 Arithmetic Circuits in .. - Grigoriev, Razborov - 1998
10 Lower Bounds on Arithmetic Circuits Via Partial Derivatives - Nisan, Wigderson - 1995
10 Negation can be Exponentially Powerful (context) - Valiant - 1980
8 Mathematical Systems Theory (context) - Shamir, Snir et al. - 1980
7 Why is Boolean Complexity Theory Di#cult (context) - Valiant - 1992
6 Feasible Arithmetic Computations: Valiant's Hypothesis (context) - Gathen - 1987
5 A Lower Bound on the Number of Additions in Monotone Computa.. (context) - Schnorr - 1976
2 The Probabiliatic Method (context) - Alon, Spencer et al. - 1992
2 Multilinear Formulas and Skepticism of Quantum Computing - Aaronson - 2004
2 Derandomizing Polynomial Identity Tests Means Proving Circui.. (context) - Impagliazzo, Kabanets - 2003
1 The Formula Size of the Determinant (context) - Kalorkoti - 1995
1 Depth-3 Arithmetic Circuits Over Fields of Characteristic Ze.. - Shpilka, Wigderson - 1999
1 Deterministic Polynomial Identity Testing in Non Commutative.. - Raz, Shpilka - 2004
Documents on the same site (http://www.wisdom.weizmann.ac.il/~ranraz/publications/index.html): More
Fourier Analysis For Probabilistic Communication Complexity - Raz (1995) (Correct)
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