具有无界扇入的对称门电路的通信矩阵的变化秩和深度下界

[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science Pub Date : 1991-09-01 DOI:10.1109/SFCS.1991.185448

Matthias Krause, S. Waack

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引用次数: 76

摘要

证明了底层具有任意对称门、顶层具有MOD/sub / m/-门的深度二电路的指数下界。这就解决了R. Smolensky(1990)提出的问题。该方法利用通信矩阵的变异秩。该方法的一种变体用于推导深度-两个电路的大小的下界，其顶部有一个阈值门

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Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in

An exponential lower bound for depth two circuits with arbitrary symmetric gates in the bottom level and with a MOD/sub m/-gate in the top level is proved. This solves a problem posed by R. Smolensky (1990). The method uses the variation rank of communication matrices. A variant of this method is used for deriving lower bounds for the size of depth-two circuits having a threshold gate at the top.<>

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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science

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