Exponential Lower Bounds for Depth Arithmetic Circuits in Algebras of Functions over Finite Fields
Résumé
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 nite eld 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).
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)