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引用次数: 876
摘要
在给定一组基本运算条件下，利用代数方法求出了基于定深无界扇入电路的不同函数复杂度的下界。特别地，我们证明了深度k的电路具有NOT, OR和MODp，其中p是素数，需要Exp(&Ogr;(n1/2k))门来计算任意r≠pm时的MODr函数。该语句包含特殊情况Yao's PARITY结果[Ya 85]和Razborov's new MAJORITY结果[Ra 86](如果1的个数能被m整除，则MODm门是输出为零的预言器)。
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fan-in circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MODp where p is a prime require Exp(&Ogr;(n1/2k)) gates to calculate MODr functions for any r ≠ pm. This statement contains as special cases Yao's PARITY result [ Ya 85 ] and Razborov's new MAJORITY result [Ra 86] (MODm gate is an oracle which outputs zero, if the number of ones is divisible by m).
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