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Lower bounds for non-commutative computation
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Why is Boolean complexity theory difficult?
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An exponential lower bound for depth 3 arithmetic circuits
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Lower bounds on arithmetic circuits via partial derivatives
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Depth-3 arithmetic circuits over fields of characteristic zero
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A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits
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A quadratic lower bound for the permanent and determinant problem over any characteristic ≠ 2
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Tensor-rank and lower bounds for arithmetic formulas
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Non-commutative circuits and the sum-of-squares problem
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Exponential time complexity of the permanent and the Tutte polynomial
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Algebraic proofs over noncommutative formulas
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Algebraic proofs over noncommutative formulas
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Reconstruction of depth-4 multilinear circuits with top fan-in 2
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Arithmetic circuit lower bounds via maxrank
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An arithmetic formula is multilinear if the polynomial computed by each of its subformulas is multilinear. We prove that any multilinear arithmetic formula for the permanent or the determinant of an n × n matrix is of size super-polynomial in n. Previously, super-polynomial lower bounds were not known (for any explicit function) even for the special case of multilinear formulas of constant depth.