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The power of negative thinking in constructing threshold circuits for addition

机译:否定思维在构建加法阈值电路中的作用

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It has recently been shown that it is possible to add two binary numbers in threshold circuits of depth two with polynomial size. It is shown here that the most significant bit of addition, which is a monotone function, needs exponential size when computed in monotone threshold circuits of depth two. In fact, it is shown that even o(n/log n) negations do not suffice for polynomial size. This is the first example of such a gap for this model.
机译:最近表明,可以在深度为二的阈值电路中以多项式大小相加两个二进制数。此处显示,当在深度为2的单调阈值电路中计算时,加法的最高有效位是单调函数,需要指数大小。实际上,已经表明,即使o(n / log n)求反也不足以满足多项式大小。这是此模型存在这种差距的第一个示例。

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