用于前缀计算的布尔网络的大小时间复杂度

G. Bilardi, F. Preparata
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引用次数: 12

摘要

前缀问题是给定一个序列x = (x0, x1,…,xN - 1),计算半群中元素的所有乘积x0x1…xj (j=0,…,N - 1)。本文完整地描述了布尔网络计算前缀的尺寸-时间复杂度。布尔网络是布尔门与一位存储设备的同步互连。这种复杂性关键取决于底层半群的一个性质,我们称之为循环自由(在半群的Cayley图中没有长度大于1的循环)。用S和T的大小和计算时间分别表示,对于非无循环半群,我们有S = &THgr;(N/T) log(N/T)),对于无循环半群,我们有S = &THgr;(N/T)。在这两种情况下,T∈[&OHgr;(logN), O(N)]。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Size-time complexity of Boolean networks for prefix computations
The prefix problem consists of computing all the products x0x1…xj (j=0, …, N - 1), given a sequence x = (x0, x1, …, xN - 1) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = &THgr;((N/T) log(N/T)), for non-cycle-free semigroups, and S = &THgr;(N/T), for cycle-free semigroups. In both cases, T ∈ [&OHgr;(logN), O(N)].
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