Catalytic branching programs from groups and general protocols

IF 0.8 Q3 COMPUTER SCIENCE, THEORY & METHODS
Hugo Côté, P. McKenzie
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引用次数: 0

Abstract

CCCatalytic branching programs (catalytic bps) compute the same n-bit boolean function f at multiple entry points that need to be remembered at the exit nodes of the bp. When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f. Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing \(\texttt {Maj} \) and \(\texttt {Mod} \) are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O(nlog n) amortized cost for any symmetric function.
组和通用协议的催化分支程序
CC催化分支程序(catalytic bps)在需要在bp的出口节点记住的多个入口点计算相同的n位布尔函数f。当允许双指数数量的进入点时,已知任何f都可以实现线性摊销催化bp大小。这里介绍了一种从可逆bp和确定性dag样通信协议中产生催化bp的方法。在低至线性的多重性范围内,以线性摊销成本近似阈值是可能的。在同样的低范围内,计算\(\texttt{Maj}\)和\(\txttt{Mod}\。在指数范围内,该方法得到O(nlog n) 任何对称函数的摊余成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACM Transactions on Computation Theory
ACM Transactions on Computation Theory COMPUTER SCIENCE, THEORY & METHODS-
CiteScore
2.30
自引率
0.00%
发文量
10
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