Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields

被引：50
|
作者：
Grigoriev, D
Razborov, A
机构：
[1] Univ Rennes 1, IMR, F-35042 Rennes, France
[2] VA Steklov Math Inst, Moscow 117966, Russia
来源：
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2000年 / 10卷 / 06期
关键词：
exponential lower bounds; depth 3 arithmetic circuits; finite fields;
D O I：
10.1007/s002009900021
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
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 subset of 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).
引用
收藏
页码：465 / 487
页数：23
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