Computer Science

Computer Science ›› 2024, Vol. 51 ›› Issue (11A): 240300161-5.doi: 10.11896/jsjkx.240300161

• Intelligent Computing • Previous Articles     Next Articles

Model Counting Method for Pseudo-Boolean Constraints

ZHENG Suhao1, NIU Qinzhou1, TAO Xiaomei2   

  1. 1 College of Information Science and Engineering,Guilin University of Technology,Guilin,Guangxi 541006,China
    2 School of Computer Science and Engineering & School of Software,Guangxi Normal University,Guilin,Guangxi 541006,China
  • Online:2024-11-16 Published:2024-11-13
  • About author:ZHENG Suhao,born in 1999,postgra-duate.His main research interests include SAT problem algorithms and theo-ry,and so on.
    NIU Qinzhou,born in 1956,Ph.D,professor.His main research interests include SAT problem algorithms,and computer network.
  • Supported by:
    National Natural Science Foundation of China(61906051).

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Abstract: Pseudo-Boolean constraints problem is a kind of combinatorial optimization problem similar to the Boolean constraints problem.The core of solving such problems lies in encoding Pseudo-Boolean constraints in different mathematical forms,such as linear programming,integer programming,and other forms of combinatorial optimization.The current popular solution is to convert the problem into Boolean formulas,and then use the conflict-oriented clause learning(CDCL) class SAT solver to solve these Boolean formulas.This paper proposes a new method to solve the model counting problem in the Pseudo-Boolean constraints problem.Firstly,the related concepts of knowledge compilation and extension rules are introduced,and then how to transform Pseudo-Boolean constraints problem into binary decision diagram(BDD) by knowledge compilation is discussed in detail,and the characteristics of BDD structure are discussed emphatically.Finally,the model counting method based on extension rules isadoptedto deal with the model counting problem in Pseudo-Boolean constraints problem.Experimental results show that the proposed method has better performance when dealing with clauses with higher complementarity factors.

Key words: Pseudo-Boolean constraints, SAT problem, Model counting, Knowledge compilation, Clause

CLC Number: 

  • TP301
[1]EÉN N,SÖRENSSON N.Translating pseudo-boolean con-straints into SAT[J].Journal on Satisfiability,Boolean Mode-ling and Computation,2006,2(1/2/3/4):1-26.
[2]ABÍO I,NIEUWENHUIS R,OLIVERAS A,et al.A new look at BDDs for pseudo-Boolean constraints[J].Journal of Artificial Intelligence Research,2012,45:443-480.
[3]BOFILL M,COLL J,NIGHTINGALE P,et al.SAT encodings for Pseudo-Boolean constraints together with at-most-one constraints[J].Artificial Intelligence,2022,302:103604.
[4]DING Z Y.Research and Implementation of Applying LinearAlgebra to Solve Satisfiability Problem[D].Guangzhou:Sun Yat-sen University,2014.
[5]FANG C,LIU J.A linear algebra formulation for boolean satis-fiability testing[J].arXiv:1701.02401,2017.
[6]HAI L,JIGUI S,YIMIN Z.Theorem proving based on the extension rule[J].Journal of Automated Reasoning,2003,31:11-21.
[7]YIN M H,LIN H,SUN J G.Solving #SAT using extensionrules[J].Journal of Software,2009,20(7):1714-1725.
[8]JHA A,SUCIU D.Knowledge compilation meets database theory:compiling queries to decision diagrams[C]//Proceedings of the 14th International Conference on Database Theory.2011:162-173.
[9]INOUE K.Evaluating abductive hypotheses using an EM algorithm on BDDs[C]//Proc.IJCAI-09.2009:810-815.
[10]DARWICHE A.Decomposable negation normal form[J].Journal of the ACM(JACM),2001,48(4):608-647.
[11]GU W X.Knowledge Compilation Survey[J].Computer Scien-ce,2010,37(7):7.
[12]ZHAO X W.Research of the Knowledge compilation and Contingent Flexible Planning[D].Changchun:Northeast Normal University,2010.
[13]LYU S,ZHANG T,WANG Q,et al.Two Novel AlgorithmsBased on Extension Rule for Solving# SAT Problem[J].Journal of Northeastern University(Natural Science),2019,40(5):630.
[14]LATOUR A L D,SEN A,MEEL K S.Solving the identifying code set problem with grouped independent support[J].arXiv:2306.15693,2023.
[15]AUSIELLO G,CRESCENZI P,GAMBOSI G,et al.Complexity and approximation:Combinatorial optimization problems and their approximability properties[M].Springer Science & Business Media,2012.
[16]ROUGHGARDEN T.Algorithmic game theory[J].Communications of the ACM,2010,53(7):78-86.
[17]DUDEK J M,PHAN V H N,VARDI M Y.DPMC:weightedmodel counting by dynamic programming on projectjoin trees[C]//International Conference on Principles and Practice of Constraint Programming.Cham:Springer International Publi-shing,2020:211-230.
[18]SUZUKI R,HASHIMOTO K,SAKAI M.Improvement of Projected Model-Counting Solver with Component Decomposition Using SAT Solving in Components:JSAI Technical Report:SIG-FPAI[R].2017:31-36.
[19]PHILIPP T,STEINKE P.Pblib-a library for encoding pseudo-boolean constraints into cnf[C]//International Conference on Theory and Applications of Satisfiability Testing.Cham:SpringerInternational Publishing,2015:9-16.
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