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Journal of Software:2015.26(9):2155-2166

基于聚类和划分的SAT分治判定
范全润,段振华
(西安电子科技大学 计算理论与技术研究所, 陕西 西安 710071;西安电子科技大学 计算理论与技术研究所, 陕西 西安 710071;ISN国家重点实验室(西安电子科技大学), 陕西 西安 710071)
Clustering and Partition Based Divide and Conquer for SAT Solving
FAN Quan-Run,DUAN Zhen-Hua
(Institute of Computing Theory and Technology, Xidian University, Xi'an 710071, China;Institute of Computing Theory and Technology, Xidian University, Xi'an 710071, China;State Key Laboratory of Integrated Services Networks (Xidian University), Xi'an 710071, China)
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Received:August 03, 2014    Revised:October 21, 2014
> 中文摘要: 提出了一种将布尔公式划分为子句组来进行布尔可满足性判定的方法.CNF(conjunctive normal form)公式是可满足的当且仅当划分产生的每个子句组都是可满足的,因此,通过判定子句组的可满足性来判定原公式的可满足性,相当于用分治法将复杂问题分解为多个子问题来求解.这种分治判定方法一方面降低了原公式的可满足性判定复杂度;另一方面,由于子句组的判定可以并行,因而判定速度能够得到进一步的提高.对于不能直接产生布尔子句组划分的情形,提出了一种利用聚类技术将CNF公式聚类成多个簇,然后消去簇间的公共变量来产生子句组划分的方法.
中文关键词: 合取范式  布尔可满足性  划分  聚类
Abstract:A partition based Boolean satisfiability solving method is proposed. By partitioning a CNF(conjunctive normal form) formula into several clause groups, Boolean satisfiability problem can be divided into small sub-problems, hence reducing the complexity of the original problem. Meanwhile, the satisfiability of different clause group can be solved in parallel, thus further speeding up the decision procedure. For the formula that clause group partition cannot be generated directly, a clustering algorithm is given to cluster clauses into clusters so that clause group partition can be generated by eliminating common variables among clusters.
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基金项目:国家自然科学基金(61133001, 61322202, 61420106004) 国家自然科学基金(61133001, 61322202, 61420106004)
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范全润,段振华.基于聚类和划分的SAT分治判定.软件学报,2015,26(9):2155-2166

FAN Quan-Run,DUAN Zhen-Hua.Clustering and Partition Based Divide and Conquer for SAT Solving.Journal of Software,2015,26(9):2155-2166