Computer Science ›› 2021, Vol. 48 ›› Issue (4): 26-30.

• Computer Science Theory •

### Community Structure of Regular (3,4)-CNF Formula

HE Bin, XU Dao-yun

1. College of Computer Science and Technology,Guizhou University,Guiyang 550025,China
• Received:2020-06-24 Revised:2021-02-03 Online:2021-04-15 Published:2021-04-09
• About author:HE Bin,born in 1995,postgraduate.His main research interests include algorithm design and analysis.(2276197035@qq.com)
XU Dao-yun,born in 1959,professor,Ph.D supervisor,is a senior member of China Computer Federation.His main research interests include computability and computational complexity.
• Supported by:
National Natural Science Foundation of China (61762019).

Abstract: By constructing an appropriate minimum unsatisfiable formula,the 3-CNF formula can be reduced and converted into a regular (3,4)-CNF formula in polynomial time.The converted regular (3,4)-CNF formula has the same satisfiability as the original 3-CNF formula.The structure of the formula has also changed accordingly.The community structure of the graph reflects the modular characteristics of the graph.The CNF formula can be transformed into the corresponding graph to study the relationship between the modular characteristics of the formula graph and some properties of the formula.The two types of formulas before and after the reduction are converted into corresponding graphs,and the module characteristics are studied.It is found that the regular (3,4)-CNF formula obtained after conversion has a high modularity.In addition,in the process of using the DPLL (Davis Putnam Logemann Loveland) algorithm to solve the CNF formula,when a conflict is encountered,the conflict-driven clause lear-ning strategy is used to obtain a learning clause and add it to the original formula,which reduces the modularity of the original formula.The research finds that when the DPLL algorithm combined with the conflict-driven clause learning strategy is applied to the regular (3,4)-CNF formula,most of the variables contained in the learning clause are located in different communities.

CLC Number:

• TP301
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