Feasible arithmetic computations: Valiant's hypothesis
Journal of Symbolic Computation
Annual review of computer science: vol. 3, 1988
Lower bounds for non-commutative computation
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
An exponential lower bound for depth 3 arithmetic circuits
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Lower bounds on arithmetic circuits via partial derivatives
Computational Complexity
Depth-3 arithmetic circuits over fields of characteristic zero
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Deterministic Polynomial Identity Testing in Non-Commutative Models
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Optimal sparse matrix dense vector multiplication in the I/O-model
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Elusive functions and lower bounds for arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Arithmetic Circuits, Syntactic Multilinearity, and the Limitations of Skew Formulae
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Lower Bounds for the Determinantal Complexity of Explicit Low Degree Polynomials
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Deterministic identity testing of depth-4 multilinear circuits with bounded top fan-in
Proceedings of the forty-second ACM symposium on Theory of computing
On the relation between polynomial identity testing and finding variable disjoint factors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors
Journal of Computer and System Sciences
On the incompressibility of monotone DNFs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Monotone multilinear boolean circuits for bipartite perfect matching require exponential size
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Separating multilinear branching programs and formulas
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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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 x 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 multi-linear formulas of constant depth.