Lower Bounds for QCDCL via Formula Gauge

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

Journal of Automated Reasoning Pub Date : 2023-09-27 DOI:10.1007/s10817-023-09683-1

Benjamin Böhm, Olaf Beyersdorff

引用次数: 3

Abstract

Abstract QCDCL is one of the main algorithmic paradigms for solving quantified Boolean formulas (QBF). We design a new technique to show lower bounds for the running time in QCDCL algorithms. For this we model QCDCL by concisely defined proof systems and identify a new width measure for formulas, which we call gauge . We show that for a large class of QBFs, large (e.g. linear) gauge implies exponential lower bounds for QCDCL proof size. We illustrate our technique by computing the gauge for a number of sample QBFs, thereby providing new exponential lower bounds for QCDCL. Our technique is the first bespoke lower bound technique for QCDCL.

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通过公式规求QCDCL的下界

QCDCL是求解量化布尔公式(QBF)的主要算法范式之一。我们设计了一种新的技术来显示QCDCL算法的运行时间下界。为此，我们用简明定义的证明系统对QCDCL进行建模，并确定了一种新的公式宽度度量，我们称之为量规。我们证明了对于一类大的QBFs，大的(例如线性)规范意味着QCDCL证明尺寸的指数下界。我们通过计算一些样本QBFs的规范来说明我们的技术，从而为QCDCL提供了新的指数下界。我们的技术是第一个定制的QCDCL下界技术。

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.