Lower bounds for matrix product, in bounded depth circuits with arbitrary gates
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Circuit and decision tree complexity of some number theoretic problems
Information and Computation
Depth-3 Arithmetic Circuits for Sn2(X) and Extensions of the Graham-Pollack Theorem
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Multi-linear formulas for permanent and determinant are of super-polynomial size
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
Circuit complexity of testing square-free numbers
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Reconstruction of depth-4 multilinear circuits with top fan-in 2
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Affine projections of polynomials: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Arithmetic circuit lower bounds via maxrank
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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A depth 3 arithmetic circuit can be viewed as a sum of products of linear functions. We prove an exponential complexity lower bound on depth 3 arithmetic circuits computing some natural symmetric functions over a finite field $F$. Also, we study the complexity of the functions $f : D^n \to F$ for subsets $D \subset F$. In particular, we prove an exponential lower bound on the complexity of a depth 3 arithmetic circuit which computes the determinant or the permanent of a matrix considered as functions $f : (F^*)^{n^2} \to F$