Should Decisions in QCDCL Follow Prefix Order?

IF 0.9 3区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Automated Reasoning Pub Date : 2024-02-09 DOI:10.1007/s10817-024-09694-6

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引用次数: 0

Abstract

Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the differences between QCDCL and propositional CDCL is that QCDCL typically follows the prefix order of the QBF for making decisions. We investigate an alternative model for QCDCL solving where decisions can be made in arbitrary order. The resulting system \(\textsf{QCDCL}^\textsf {{A\tiny {\MakeUppercase {ny}}}}\) is still sound and terminating, but does not necessarily allow to always learn asserting clauses or cubes. To address this potential drawback, we additionally introduce two subsystems that guarantee to always learn asserting clauses ( \(\textsf{QCDCL}^\textsf {{U\tiny {\MakeUppercase {ni}}-A\tiny {\MakeUppercase {ny}}}}\) ) and asserting cubes ( \(\textsf{QCDCL}^\textsf {{E\tiny {\MakeUppercase {xi}}-A\tiny {\MakeUppercase {ny}}}}\) ), respectively. We model all four approaches by formal proof systems and show that \(\textsf{QCDCL}^\textsf {{U\tiny {\MakeUppercase {ni}}-A\tiny {\MakeUppercase {ny}}}}\) is exponentially better than \(\mathsf{{QCDCL}} \) on false formulas, whereas \(\textsf{QCDCL}^\textsf {{E\tiny {\MakeUppercase {xi}}-A\tiny {\MakeUppercase {ny}}}}\) is exponentially better than \(\mathsf{{QCDCL}} \) on true QBFs. Technically, this involves constructing specific QBF families and showing lower and upper bounds in the respective proof systems. We complement our theoretical study with some initial experiments that confirm our theoretical findings.

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QCDCL 中的决定是否应遵循前缀顺序？

摘要量化冲突驱动子句学习（QCDCL）是量化布尔公式（QBF）的主要求解方法之一。QCDCL 与命题 CDCL 的区别之一是，QCDCL 通常按照 QBF 的前缀顺序进行决策。我们研究了另一种 QCDCL 解题模型，在这种模型中，决策可以按照任意顺序做出。由此产生的系统（\textsf{QCDCL}^\textsf {{A\tiny {\MakeUppercase {ny}}}}）仍然是健全的、终止的，但并不一定总是允许学习断言子句或立方体。为了解决这个潜在的缺陷、我们还引入了两个子系统来保证总是学习断言子句（\(\textsf{QCDCL}^\textsf {{U\tiny {\MakeUppercase {ni}}-A\tiny {\MakeUppercase {ny}}}}\) ）和断言立方（（\textsf{QCDCL}^\textsf {{E\tiny {\MakeUppercase {xi}}-A\tiny {\MakeUppercase {ny}}}}\) ）、分别。我们用形式化证明系统对这四种方法进行了建模，并证明在假公式上，\(\textsf{QCDCL}^\textsf {{U\tiny {MakeUppercase {ni}}-A\tiny {MakeUppercase {ny}}}}\) 比\(\mathsf{QCDCL}}\)要好很多、而在真（QBF）上，textsf{QCDCL}^textsf {{E\tiny {MakeUppercase {xi}}-A\tiny {MakeUppercase {ny}}}}\) 比 \(\mathsf{{QCDCL}} \)好很多。从技术上讲，这需要构建特定的 QBF 族，并在各自的证明系统中显示下限和上限。我们用一些初步实验来补充我们的理论研究，这些实验证实了我们的理论发现。

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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来源期刊

Journal of Automated Reasoning 工程技术-计算机：人工智能

CiteScore

3.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning. The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.