Learning DNF by approximating inclusion-exclusion formulae

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-04 DOI:10.1109/CCC.1999.766279

J. Tarui, Tatsuie Tsukiji

引用次数: 23

Abstract

We analyze upper and lower bounds on size of Boolean conjunctions necessary and sufficient to approximate a given DNF formula by accuracy slightly better than 1/2 (here we define the size of a Boolean conjunction as the number of distinct variables on which it depends). Such an analysis determines the performance of a naive search algorithm that exhausts Boolean conjunctions in the order of their sizes. In fact, our analysis does not depend on kinds of symmetric functions to be exhausted: instead of conjunctions, counting either disjunctions, parity functions, majority functions, or even general symmetric functions, derives the same learning results from similar analyses.

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通过近似包容-排除公式学习DNF

我们分析了布尔连接大小的上界和下界，这是近似给定DNF公式的必要和充分条件，精度略高于1/2(这里我们将布尔连接的大小定义为它所依赖的不同变量的数量)。这样的分析决定了朴素搜索算法的性能，该算法按大小顺序耗尽布尔连词。事实上，我们的分析并不依赖于要耗尽的对称函数的种类:而不是连词，计算析取，宇称函数，多数函数，甚至一般对称函数，从类似的分析中得出相同的学习结果。

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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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

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