Evaluation of Monotone DNF Formulas

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• 作者：Sarah R. Allen ; Lisa Hellerstein ; Devorah Kletenik ; Tonguç Ünlüyurt
• 关键词：DNF formulas ; Sequential testing ; Stochastic boolean function evaluation ; Approximation algorithms
• 刊名：Algorithmica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：77
• 期：3
• 页码：661-685
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Inform
• 出版者：Springer US
• ISSN：1432-0541
• 卷排序：77

文摘

Stochastic boolean function evaluation (SBFE) is the problem of determining the value of a given boolean function f on an unknown input x, when each bit \(x_i\) of x can only be determined by paying a given associated cost \(c_i\). Further, x is drawn from a given product distribution: for each \(x_i\), \(\mathbf{Pr}[x_i=1] = p_i\) and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution.