一种布尔公式的代数逻辑约化新方法

doi:10.11896/jsjkx.190400018

计算机科学 ›› 2020, Vol. 47 ›› Issue (5): 32-37.doi: 10.11896/jsjkx.190400018

所属专题：理论计算机科学

一种布尔公式的代数逻辑约化新方法

刘江, 周鸿昊

中国科学院重庆绿色智能技术研究院高性能计算应用研究中心重庆400714
中国科学院大学北京100049

收稿日期:2019-03-02 出版日期:2020-05-15 发布日期:2020-05-19
通讯作者: 刘江(liujiang@cigit.ac.cn)
基金资助:
国家自然科学基金(61672488)

New Algebraic Logic Reduction Method for Boolean Formula

LIU Jiang, ZHOU Hong-hao

High Performance Computing Application Research Center,Chongqing Institute of Green and Intelligent Technology,Chinese Academy of ences,Chongqing 400714,China
University of Chinese Academy of Sciences,Beijing 100049,China

Received:2019-03-02 Online:2020-05-15 Published:2020-05-19
About author:LIU Jiang,born in 1979,Ph.D,associate professor,is a member of China Computer Federation.His main research interests include computability theory,formal methods and computer algorithms.
Supported by:
This work was supported by the National Natural Science Foundation of China (61672488)

摘要/Abstract

摘要： 布尔可满足问题是最早被证明的NP完全问题之一,1-in-3-SAT问题是一个NP完全的布尔可满足子类问题。1-in-3-SAT的计算复杂度取决于对应公式的变量以及子句的个数。将1-in-3公式归约为一个变量数或者子句数更少的1-in-3公式,是提高1-in-3-SAT问题求解效率的一个关键。基于一个新的范式形式——XCNF,针对1-in-3-SAT问题提出一种新的代数逻辑约化方法,用于在多项式时间内约减一个1-in-3公式的变量数和子句数。所提算法的主要思想为:首先将1-in-3公式转化为XCNF公式,然后尝试找出XCNF公式中的X-纯文字,并利用X-纯文字法则对1-in-3公式中相应的布尔变量赋值,最后得到一个约减公式,该约减公式与原公式的1-in-3可满足性等价。

关键词: 1-in-3-SAT, NP完全问题, XCNF, X-纯文字, 布尔可满足性问题

Abstract: Boolean satisfiability problem is one of the earliest proven NP complete problem.1-in-3-SAT problem is an NP complete subclass of Boolean satisfiability problem.The computational complexity of 1-in-3-SAT depends on the number of the variables and clauses in the formula.How to reduce the 1-in-3 formula to one with less variables or clauses is the key to improve the efficiency of solving 1-in-3-SAT.Based on a new type of normal form－XCNF,this paper proposes a new algebraic logic reduction method to reduce the number of variables and clauses in polynomial time.The main idea is as follows.First,the method transforms the 1-in-3 formula into a XCNF formula,then tries to find out the X pure literal in the XCNF formula and assign the corresponding Boolean variable in the 1-in-3 formula with X pure literal rule.At last,a reduced formula which has the same 1-in-3 satisfiability with the original one can be obtained.

Key words: 1-in-3-SAT, Boolean satisfiability problem, NP complete problem, X pure literal, XCNF

中图分类号:

TP311

刘江, 周鸿昊. 一种布尔公式的代数逻辑约化新方法[J]. 计算机科学, 2020, 47(5): 32-37. https://doi.org/10.11896/jsjkx.190400018

LIU Jiang, ZHOU Hong-hao. New Algebraic Logic Reduction Method for Boolean Formula[J]. Computer Science, 2020, 47(5): 32-37. https://doi.org/10.11896/jsjkx.190400018

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一种布尔公式的代数逻辑约化新方法

New Algebraic Logic Reduction Method for Boolean Formula

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