In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic...In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic Filtering method that consists of two restriction rules for FLD: internal and external filtering. The method reduces the number of tested literals in FLD and its computational time while maintaining the ability to find most of the failed literals in each decision level. Unlike the pre-defined criteria, literals are removed dynamically in our approach. In this way, our FLD can adapt itself to different real-life benchmarks. Many useless tests are therefore avoided and as a consequence it makes FLD fast. Some other static restrictions are also added to further improve the efficiency of FLD. Experiments show that our optimized FLD is much more efficient than other advanced reasoning techniques.展开更多
This paper reviews the recent literature on solving the Boolean satisfiability problem(SAT),an archetypal N P-complete problem,with the aid of machine learning(ML)techniques.Over the last decade,the machine learning s...This paper reviews the recent literature on solving the Boolean satisfiability problem(SAT),an archetypal N P-complete problem,with the aid of machine learning(ML)techniques.Over the last decade,the machine learning society advances rapidly and surpasses human performance on several tasks.This trend also inspires a number of works that apply machine learning methods for SAT solving.In this survey,we examine the evolving ML SAT solvers from naive classifiers with handcrafted features to emerging end-to-end SAT solvers,as well as recent progress on combinations of existing conflict-driven clause learning(CDCL)and local search solvers with machine learning methods.Overall,solving SAT with machine learning is a promising yet challenging research topic.We conclude the limitations of current works and suggest possible future directions.The collected paper list is available at https://github.com/ThinklabSJTU/awesome-ml4co.Keywords:Machine learning(ML),Boolean satisfiability(SAT),deep learning,graph neural networks(GNNs),combinatorial optimization.展开更多
As a complementary technology to Binary Decision Diagram-based(BDD-based) symbolic model checking, the verification techniques on Boolean satisfiability problem have gained an increasing wide of applications over the ...As a complementary technology to Binary Decision Diagram-based(BDD-based) symbolic model checking, the verification techniques on Boolean satisfiability problem have gained an increasing wide of applications over the last few decades, which brings a dramatic improvement for automatic verification. In this paper, we firstly introduce the theory about the Boolean satisfiability verification, including the description on the problem of Boolean satisfiability verification, Davis-Putnam-Logemann-Loveland(DPLL) based complete verification algorithm, and all kinds of solvers generated and the logic languages used by those solvers. Moreover, we formulate a large number optimizations of technique revolutions based on Boolean SATisfiability(SAT) and Satisfiability Modulo Theories(SMT) solving in detail, including incomplete methods such as bounded model checking, and other methods for concurrent programs model checking. Finally, we point out the major challenge pervasively in industrial practice and prospect directions for future research in the field of formal verification.展开更多
提出了一项新的正向推理技术:对称扩展的一元子句推导(Symmetric Extended Unit Propagation)。与传统的一元子句推导技术相比,文中的方法通过在一元子句推导过程中添加对称的蕴涵关系从而能够推导出更多的一元子句。基于这项新技术实...提出了一项新的正向推理技术:对称扩展的一元子句推导(Symmetric Extended Unit Propagation)。与传统的一元子句推导技术相比,文中的方法通过在一元子句推导过程中添加对称的蕴涵关系从而能够推导出更多的一元子句。基于这项新技术实现了一个可满足性问题(SAT)预处理器Snowball。实验结果验证了该项技术的有效性,表明该预处理器Snowball能够有效地化简SAT问题的规模并减少解决SAT问题的时间。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.90207002 and 60176017)the National High Technology Research and Development 863 Plan(Grant Nos.2002AAIZ1460,2002AA1Z1340 and 2002AA1Z1460)NSF(Grant Nos.CCR-0098275 and CCR-0306298).
文摘In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic Filtering method that consists of two restriction rules for FLD: internal and external filtering. The method reduces the number of tested literals in FLD and its computational time while maintaining the ability to find most of the failed literals in each decision level. Unlike the pre-defined criteria, literals are removed dynamically in our approach. In this way, our FLD can adapt itself to different real-life benchmarks. Many useless tests are therefore avoided and as a consequence it makes FLD fast. Some other static restrictions are also added to further improve the efficiency of FLD. Experiments show that our optimized FLD is much more efficient than other advanced reasoning techniques.
基金supported by National Key Research and Development Program of China(No.2020AAA0107600)National Science Foundation of China(No.62102258)+2 种基金Shanghai Pujiang Program,China(No.21PJ1407300)Shanghai Municipal Science and Technology Major Project,China(No.2021SHZDZX0102)Science and Technology Commission of Shanghai Municipality Project,China(No.22511105100),and also sponsored by Huawei Ltd,China.
文摘This paper reviews the recent literature on solving the Boolean satisfiability problem(SAT),an archetypal N P-complete problem,with the aid of machine learning(ML)techniques.Over the last decade,the machine learning society advances rapidly and surpasses human performance on several tasks.This trend also inspires a number of works that apply machine learning methods for SAT solving.In this survey,we examine the evolving ML SAT solvers from naive classifiers with handcrafted features to emerging end-to-end SAT solvers,as well as recent progress on combinations of existing conflict-driven clause learning(CDCL)and local search solvers with machine learning methods.Overall,solving SAT with machine learning is a promising yet challenging research topic.We conclude the limitations of current works and suggest possible future directions.The collected paper list is available at https://github.com/ThinklabSJTU/awesome-ml4co.Keywords:Machine learning(ML),Boolean satisfiability(SAT),deep learning,graph neural networks(GNNs),combinatorial optimization.
基金Supported by the National Natural Science Foundation of China(Nos.61063002,61100186,61262008)Guangxi Natural Science Foundation of China(2011GXNSFA018164,2011GXNSFA018166,2012GXNSFAA053220)the Key Project of Education Department of Guangxi
文摘As a complementary technology to Binary Decision Diagram-based(BDD-based) symbolic model checking, the verification techniques on Boolean satisfiability problem have gained an increasing wide of applications over the last few decades, which brings a dramatic improvement for automatic verification. In this paper, we firstly introduce the theory about the Boolean satisfiability verification, including the description on the problem of Boolean satisfiability verification, Davis-Putnam-Logemann-Loveland(DPLL) based complete verification algorithm, and all kinds of solvers generated and the logic languages used by those solvers. Moreover, we formulate a large number optimizations of technique revolutions based on Boolean SATisfiability(SAT) and Satisfiability Modulo Theories(SMT) solving in detail, including incomplete methods such as bounded model checking, and other methods for concurrent programs model checking. Finally, we point out the major challenge pervasively in industrial practice and prospect directions for future research in the field of formal verification.
文摘提出了一项新的正向推理技术:对称扩展的一元子句推导(Symmetric Extended Unit Propagation)。与传统的一元子句推导技术相比,文中的方法通过在一元子句推导过程中添加对称的蕴涵关系从而能够推导出更多的一元子句。基于这项新技术实现了一个可满足性问题(SAT)预处理器Snowball。实验结果验证了该项技术的有效性,表明该预处理器Snowball能够有效地化简SAT问题的规模并减少解决SAT问题的时间。
