Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields
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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 →F for subsets D⊂F. In particular, we prove an exponential lower bound on the complexity of depth 3 arithmetic circuits computing some explicit functions f:(F*) n →F (in particular, the determinant of a matrix).
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