Pseudorandom generators for width-3 branching programs
Pseudorandom generators for width-3 branching programs
复制标题
用于宽度 3 分支程序的伪随机生成器
DOI：
10.1145/3313276.3316319
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Avishay Tal
中科院分区：
文献类型：
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作者：
Raghu Meka;Omer Reingold;Avishay Tal
我们构建了种子长度的伪andom生成器（log（n）·log（1/є）），with 3和长度为n，我们使用pseudorandom Generators的宽度读取式分支程序（ROBPS）。种子长度（log（n）·poly（1/є）。 Gopalan等人的“迭代米勒限制”。 Braverman等人[Sicomp，2014年]。在我们的分析中的重要作用是：（1）一种重新标记的技术，使我们能够分析给定的分支程序的重新标记版本，事实证明（2）将分支程序中的碰撞层数量视为进度。测量并表明它在伪和限制下大大降低了。长度为n和宽度3（概括读取对接的CNF和DNF）的局部 - 单身剂机器人，以及（3）在每个连续的polygog（n）层中具有宽度2层的恒定长度n层。
We construct pseudorandom generators of seed length Õ(log(n)· log(1/є)) that є-fool ordered read-once branching programs (ROBPs) of width 3 and length n. For unordered ROBPs, we construct pseudorandom generators with seed length Õ(log(n) · poly(1/є)). This is the first improvement for pseudorandom generators fooling width 3 ROBPs since the work of Nisan [Combinatorica, 1992]. Our constructions are based on the “iterated milder restrictions” approach of Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered case, we combine iterated milder restrictions with the generator of Chattopadhyay et al. [CCC, 2018]. Two conceptual ideas that play an important role in our analysis are: (1) A relabeling technique allowing us to analyze a relabeled version of the given branching program, which turns out to be much easier. (2) Treating the number of colliding layers in a branching program as a progress measure and showing that it reduces significantly under pseudorandom restrictions. In addition, we achieve nearly optimal seed-length Õ(log(n/є)) for the classes of: (1) read-once polynomials on n variables, (2) locally-monotone ROBPs of length n and width 3 (generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length n having a layer of width 2 in every consecutive polylog(n) layers.
用于以任意顺序读取一次的分支程序的伪随机生成器
DOI：
10.1109/focs.2018.00093
发表时间：
2018
期刊：
59th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2018
影响因子：
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作者：
Forbes, Michael A.;Kelley, Zander
通讯作者：
Kelley, Zander