求解QBF的硬公式类

IF 4.5 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Artificial Intelligence Research Pub Date : 2023-08-14 DOI:10.1613/jair.1.14710

Agnes Schleitzer, Olaf Beyersdorff

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引用次数: 0

摘要

到目前为止，我们只知道一些手工制作的量化布尔公式(QBF)，这些公式很难用于Q-Res和Q-Res等中央QBF分解系统，并且只有一个特定的QBF家族来分离Q-Res和Q-Res。本文给出了构造Q-Res和Q-Res硬公式的一般方法。结构使用简单的命题公式(例如，最小不满意公式)与简单的QBF小工具(Σb2公式没有恒定的获胜策略)相结合。这导致了一系列新的硬公式，包括硬随机qbf的新类别。我们进一步给出了Q-Res和Q-Res以及Q-Res和LD-Q-Res分离公式的一般结构。

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Classes of Hard Formulas for QBF Resolution

To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q-Res and QU-Res, and only one specific QBF family to separate Q-Res and QU-Res. Here we provide a general method to construct hard formulas for Q-Res and QU-Res. The construction uses simple propositional formulas (e.g. minimally unsatisfiable formulas) in combination with easy QBF gadgets (Σb2 formulas without constant winning strategies). This leads to a host of new hard formulas, including new classes of hard random QBFs. We further present generic constructions for formulas separating Q-Res and QU-Res, and for separating Q-Res and LD-Q-Res.

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来源期刊

Journal of Artificial Intelligence Research 工程技术-计算机：人工智能

CiteScore

9.60

自引率

4.00%

发文量

审稿时长

4 months

期刊介绍： JAIR(ISSN 1076 - 9757) covers all areas of artificial intelligence (AI), publishing refereed research articles, survey articles, and technical notes. Established in 1993 as one of the first electronic scientific journals, JAIR is indexed by INSPEC, Science Citation Index, and MathSciNet. JAIR reviews papers within approximately three months of submission and publishes accepted articles on the internet immediately upon receiving the final versions. JAIR articles are published for free distribution on the internet by the AI Access Foundation, and for purchase in bound volumes by AAAI Press.