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
SAT-based bounded model checking （BMC） has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approac...SAT-based bounded model checking （BMC） has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approach was first introduced by A. Biere et al. in checking linear temporal logic （LTL） formulae and then also adapted to check formulae of the universal fragment of computation tree logic （ACTL） by W. Penczek et al. As the efficiency of model checking is still an important issue, we present an improved BMC approach for ACTL based on Penczek＇s method. We consider two aspects of the approach. One is reduction of the number of variables and transitions in the κ-model by distinguishing the temporal operator EX from the others. The other is simplification of the transformation of formulae by using uniform path encoding instead of a disjunction of all paths needed in the κ-model. With these improvements, for an ACTL formula, the length of the final encoding of the formula in the worst case is reduced. The improved approach is implemented in the tool BMV and is compared with the original one by applying both to two well known examples, mutual exclusion and dining philosophers. The comparison shoves the advantages of the improved approach with respect to the efficiency of model checking.展开更多
G(p)和G(p→F(q))是有界模型检测(bounded model checking,简称BMC)中的两个重要的常用模态算子.对验证G(p)和G(p→F(q))编码转换公式进行优化.通过分析当验证这些模态算子时FSM(finite state machine)的状态转移和线性时序逻辑(linear-...G(p)和G(p→F(q))是有界模型检测(bounded model checking,简称BMC)中的两个重要的常用模态算子.对验证G(p)和G(p→F(q))编码转换公式进行优化.通过分析当验证这些模态算子时FSM(finite state machine)的状态转移和线性时序逻辑(linear-time temporal logic,简称LTL)的语义特征.在现有的编码公式的基础上,给出了简洁、高效的递推公式,该公式有利于高效编码成SAT(satisfiability)实例;证明了递推公式和原转换公式的逻辑关系.通过实验比较分析,在生成SAT实例规模和易求解方面都优于BMC中求解这些模态算子的现有的两种重要方法AA_BMC和Timo_BMC.所给出的方法和思想对于BMC中验证其他模态算子时的编码优化也有参考价值.展开更多
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.
基金supported by the National Natural Science Foundation of China under Grants No.60573012 and No.60721061the National Basic Research 973 Program of China under Grant No.2002CB312200.
文摘SAT-based bounded model checking （BMC） has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approach was first introduced by A. Biere et al. in checking linear temporal logic （LTL） formulae and then also adapted to check formulae of the universal fragment of computation tree logic （ACTL） by W. Penczek et al. As the efficiency of model checking is still an important issue, we present an improved BMC approach for ACTL based on Penczek＇s method. We consider two aspects of the approach. One is reduction of the number of variables and transitions in the κ-model by distinguishing the temporal operator EX from the others. The other is simplification of the transformation of formulae by using uniform path encoding instead of a disjunction of all paths needed in the κ-model. With these improvements, for an ACTL formula, the length of the final encoding of the formula in the worst case is reduced. The improved approach is implemented in the tool BMV and is compared with the original one by applying both to two well known examples, mutual exclusion and dining philosophers. The comparison shoves the advantages of the improved approach with respect to the efficiency of model checking.
文摘G(p)和G(p→F(q))是有界模型检测(bounded model checking,简称BMC)中的两个重要的常用模态算子.对验证G(p)和G(p→F(q))编码转换公式进行优化.通过分析当验证这些模态算子时FSM(finite state machine)的状态转移和线性时序逻辑(linear-time temporal logic,简称LTL)的语义特征.在现有的编码公式的基础上,给出了简洁、高效的递推公式,该公式有利于高效编码成SAT(satisfiability)实例;证明了递推公式和原转换公式的逻辑关系.通过实验比较分析,在生成SAT实例规模和易求解方面都优于BMC中求解这些模态算子的现有的两种重要方法AA_BMC和Timo_BMC.所给出的方法和思想对于BMC中验证其他模态算子时的编码优化也有参考价值.
文摘状态迁移矩阵(State Transition Matrix,STM)是一种基于表结构的程序建模语言。事件变量类型单一,事件和状态数量的增加很容易造成状态空间爆炸问题,无法表达具有时间语义的软件系统等原因,极大限制了该建模方法的推广应用。文中针对这些问题,首先提出层次化时间状态迁移矩阵(Hierarchical Time State Transition Matrix,HTSTM)模型,用于设计、建模和验证具有时间条件约束的软件系统,并给出形式化表示方法。基于该表示方法提出一种符号化编码方法,采用有界模型检测思想将需要验证的LTL性质输入SMT(Satisfiability Modulo Theories)求解器进行验证,从而在一定程度上证明了软件设计的正确性。
