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114
Interpolation and SATbased model checking
, 2003
"... Abstract. We consider a fully SATbased method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDDbased symbolic model checking, and compares f ..."
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Cited by 196 (9 self)
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Abstract. We consider a fully SATbased method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDDbased symbolic model checking, and compares favorably to some recent SATbased model checking methods on positive instances. 1
Applying SAT methods in unbounded symbolic model checking
, 2002
"... Abstract. A method of symbolic model checking is introduced that uses conjunctive normal form (CNF) rather than binary decision diagrams (BDD’s) and uses a SATbased approach to quantifier elimination. This method is compared to a traditional BDDbased model checking approach using a set of benchmar ..."
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Cited by 125 (2 self)
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Abstract. A method of symbolic model checking is introduced that uses conjunctive normal form (CNF) rather than binary decision diagrams (BDD’s) and uses a SATbased approach to quantifier elimination. This method is compared to a traditional BDDbased model checking approach using a set of benchmark problems derived from the compositional verification of a commercial microprocessor design. 1
SATbased Verification without State Space Traversal
 In Formal Methods in ComputerAided Design
, 2000
"... . Binary Decision Diagrams (BDDs) have dominated the area of symbolic model checking for the past decade. Recently, the use of satisfiability (SAT) solvers has emerged as an interesting complement to BDDs. SATbased methods are capable of coping with some of the systems that BDDs are unable to h ..."
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Cited by 66 (3 self)
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. Binary Decision Diagrams (BDDs) have dominated the area of symbolic model checking for the past decade. Recently, the use of satisfiability (SAT) solvers has emerged as an interesting complement to BDDs. SATbased methods are capable of coping with some of the systems that BDDs are unable to handle. The most challenging problem that has to be solved in order to adapt standard symbolic model checking to SATsolvers is the boolean quantification necessary for traversing the state space. A possible approach to extending the applicability of SATbased model checkers is therefore to reduce the amount of traversal. In this paper, we investigate a BDDbased verification algorithm due to van Eijk. Van Eijk's algorithm tries to compute information that is sufficient to prove a given safety property directly. When this is not possible, the computed information can be used to reduce the amount of traversal needed by standard model checking algorithms. We convert van Eijk's algori...
Conflict driven learning in a quantified Boolean satisfiability solver
 in ICCAD ’02: Proceedings of the 2002 IEEE/ACM international conference on Computeraided design
, 2002
"... Within the verification community, there has been a recent increase in interest in Quantified Boolean Formula evaluation (QBF) as many interesting sequential circuit verification problems can be formulated as QBF instances. A closely related research area to QBF is Boolean Satisfiability (SAT). Rece ..."
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Cited by 61 (3 self)
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Within the verification community, there has been a recent increase in interest in Quantified Boolean Formula evaluation (QBF) as many interesting sequential circuit verification problems can be formulated as QBF instances. A closely related research area to QBF is Boolean Satisfiability (SAT). Recent advances in SAT research have resulted in some very efficient SAT solvers. One of the critical techniques employed in these solvers is Conflict Driven Learning. In this paper, we adapt conflict driven learning for application in a QBF setting. We show that conflict driven learning can be regarded as a resolution process on the clauses. We prove that under certain conditions, tautology clauses obtained from resolution in QBF also obey the rules for implication and conflicts of regular (nontautology) clauses; and therefore they can be treated as regular clauses and used in future search. We have implemented this idea in a new QBF solver called Quaffle and our initial experiments show that conflict driven learning can greatly speed up the solution process for most of the benchmarks we tested. 1.
Temporal Induction by Incremental SAT Solving
, 2003
"... We show how a very modest modi cation to a typical modern SATsolver enables it to solve a series of related SATinstances eciently. ..."
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Cited by 58 (2 self)
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We show how a very modest modi cation to a typical modern SATsolver enables it to solve a series of related SATinstances eciently.
Bounded model checking and induction: From refutation to verification (extended abstract, category A
 Proceedings of the 15th International Conference on Computer Aided Verification, CAV 2003, volume 2725 of Lecture Notes in Computer Science
"... Abstract. We explore the combination of bounded model checking and induction for proving safety properties of infinitestate systems. In particular, we define a general kinduction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are gen ..."
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Cited by 51 (8 self)
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Abstract. We explore the combination of bounded model checking and induction for proving safety properties of infinitestate systems. In particular, we define a general kinduction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed kinduction proofs. This strengthening step requires quantifierelimination, and we propose a lazy quantifierelimination procedure, which delays expensive computations of disjunctive normal forms when possible. The effectiveness of induction based on bounded model checking and invariant strengthening is demonstrated using infinitestate systems ranging from communication protocols to timed automata and (linear) hybrid automata. 1 Introduction Bounded model checking (BMC) [5, 4, 7] is often used for refutation, where one systematically searches for counterexamples whose length is bounded by some integer k. The bound k is increased until a bug is found, or some precomputed completeness threshold is reached. Unfortunately, the computation of completeness thresholds is usually prohibitively expensive and these thresholds may be too large to effectively explore the associated bounded search space. In addition, such completeness thresholds do not exist for many infinitestate systems.
Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation
, 2002
"... In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the DavisPutnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, impli ..."
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Cited by 48 (2 self)
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In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the DavisPutnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, implications are generated from these clauses, and backtracking in the search tree is chronological. In this work, we augment the basic DPLL algorithm with conflict driven learning as well as satisfiability directed implication and learning. In addition to the traditional clause database, we add a cube database to the data structure. We show that cubes can be used to generate satisfiability directed implications similar to conflict directed implications generated by the clauses. We show that in a QBF setting, conflicting leaves and satisfying leaves of the search tree both provide valuable information to the solver in a symmetric way. We have implemented our algorithm in the new QBF solver Quaffle. Experimental results show that for some test cases, satisfiability directed implication and learning significantly prunes the search.
Property Checking via Structural Analysis
 in ComputerAided Verification
, 2002
"... Abstract. This paper describes a structurallyguided framework for the decomposition of a verification task into subtasks, each solved by a specialized algorithm for overall efficiency. Our contributions include the following: (1) a structural algorithm for computing a bound of a statetransition di ..."
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Cited by 41 (8 self)
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Abstract. This paper describes a structurallyguided framework for the decomposition of a verification task into subtasks, each solved by a specialized algorithm for overall efficiency. Our contributions include the following: (1) a structural algorithm for computing a bound of a statetransition diagram’s diameter which, for several classes of netlists, is sufficiently small to guarantee completeness of a bounded property check; (2) a robust backward unfolding technique for structural target enlargement: from the target states, we perform a series of composebased preimage computations, truncating the search if resource limitations are exceeded; (3) similar to frontier simplification in symbolic reachability analysis, we use induction via don’t cares for enhancing the presented target enlargement. In many practical cases, the verification problem can be discharged by the enlargement process; otherwise, it is passed in simplified form to an arbitrary subsequent solution approach. The presented techniques are embedded in a flexible verification framework, allowing arbitrary combinations with other techniques. Extensive experimental results demonstrate the effectiveness of the described methods at solving and simplifying practical verification problems. 1
Applications of Craig interpolants in model checking
 In TACAS’2005: Tools and Algorithms for the Construction and Analysis of Systems, LNCS 3440
, 2005
"... Abstract. A Craig interpolant for a mutually inconsistent pair of formulas (A, B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. An interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and pro ..."
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Cited by 33 (0 self)
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Abstract. A Craig interpolant for a mutually inconsistent pair of formulas (A, B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. An interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. We will discuss a number of applications of this concept in finite and infinitestate model checking. 1
Dynamic Transition Relation Simplification for Bounded Property Checking
, 2004
"... Bounded Model Checking (BMC) is an incomplete property checking method that is based on a finite unfolding of the transition relation to disprove the correctness of a set of properties or to prove them for a limited execution lengths from the initial states. Current BMC techniques repeatedly concate ..."
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Cited by 32 (2 self)
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Bounded Model Checking (BMC) is an incomplete property checking method that is based on a finite unfolding of the transition relation to disprove the correctness of a set of properties or to prove them for a limited execution lengths from the initial states. Current BMC techniques repeatedly concatenate the original transition relation to unfold the circuit with increasing depths. In this paper we present a new method that is based on a dual unfolding scheme. The first unfolding is noninitialized and progressively simplifies concatenated frames of the transition relation. The tail of the simplified frames are then applied in the second unfolding, which starts from the initial state and checks the properties. We use a circuit graph representation for all functions and performs simplification by merging vertices that are functionally equivalent under given input constraints. In the noninitialized unfolding, previous time frames progressively tighten these constraints thus leading to an asymptotic simplification of the transition relation. As a side benefit, our method can find inductive invariants constructively by detecting when vertices are functionally equivalent across time frames. This information is then used to further simplify the transition relation and, in some cases, prove unbounded correctness of properties. Our experiments using industrial property checking problems demonstrate that the presented method significantly improves the efficiency of BMC.