精确学习读取两次DNF公式

Howard Aizenstein, L. Pitt
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引用次数: 55

摘要

提出了一种多项式时间算法,用于精确学习读两次DNF公式,即每个变量最多出现两次的析取范式布尔公式。所使用的(标准)协议允许学习算法查询布尔变量的给定赋值是否满足要学习的DNF公式(成员查询),以及获取其当前假设正确性的反例,该假设可以是任意DNF公式(等价查询)。学习算法输出的公式与要学习的公式在逻辑上是等价的。
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Exact learning of read-twice DNF formulas
A polynomial-time algorithm is presented for exactly learning the class of read-twice DNF formulas, i.e. Boolean formulas in disjunctive normal form where each variable appears at most twice. The (standard) protocol used allows the learning algorithm to query whether a given assignment of Boolean variables satisfies the DNF formula to be learned (membership queries), as well as to obtain counterexamples to the correctness of its current hypothesis which can be any arbitrary DNF formula (equivalence queries). The formula output by the learning algorithm is logically equivalent to the formula to be learned.<>
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