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
提出了一种将布尔公式划分为子句组来进行布尔可满足性判定的方法.CNF(conjunctive normal form)公式是可满足的当且仅当划分产生的每个子句组都是可满足的,因此,通过判定子句组的可满足性来判定原公式的可满足性,相当于用分治法将复杂...提出了一种将布尔公式划分为子句组来进行布尔可满足性判定的方法.CNF(conjunctive normal form)公式是可满足的当且仅当划分产生的每个子句组都是可满足的,因此,通过判定子句组的可满足性来判定原公式的可满足性,相当于用分治法将复杂问题分解为多个子问题来求解.这种分治判定方法一方面降低了原公式的可满足性判定复杂度;另一方面,由于子句组的判定可以并行,因而判定速度能够得到进一步的提高.对于不能直接产生布尔子句组划分的情形,提出了一种利用聚类技术将CNF公式聚类成多个簇,然后消去簇间的公共变量来产生子句组划分的方法.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.
文摘提出了一种将布尔公式划分为子句组来进行布尔可满足性判定的方法.CNF(conjunctive normal form)公式是可满足的当且仅当划分产生的每个子句组都是可满足的,因此,通过判定子句组的可满足性来判定原公式的可满足性,相当于用分治法将复杂问题分解为多个子问题来求解.这种分治判定方法一方面降低了原公式的可满足性判定复杂度;另一方面,由于子句组的判定可以并行,因而判定速度能够得到进一步的提高.对于不能直接产生布尔子句组划分的情形,提出了一种利用聚类技术将CNF公式聚类成多个簇,然后消去簇间的公共变量来产生子句组划分的方法.