一次读取公式的求和:有多少个被加数就足够了?
Sums of read-once formulas: How many summands suffice?
摘要:
算术只读公式(ROF)是$+,\times$上的公式(扇出1的电路),其中每个变量标记至多一个叶。每个多线性多项式可以表示为ROF的和。在这项工作中,我们证明了,某些多线性多项式,在这样的表达式的被加数的紧下界。
英文摘要:
An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over $+,\times$ where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression.
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