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150
Picosat essentials
 Journal on Satisfiability, Boolean Modeling and Computation (JSAT
"... In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this lowlevel optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces ..."
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Cited by 79 (9 self)
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In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this lowlevel optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces compactly in memory and further unique features of PicoSAT including an aggressive restart schedule. Keywords: SAT solver, watched literals, occurrence lists, proof traces, restarts
Lazy abstraction with interpolants
 In Proc. CAV, LNCS 4144
, 2006
"... Abstract. We describe a model checker for infinitestate sequential programs, based on Craig interpolation and the lazy abstraction paradigm. On device driver benchmarks, we observe a speedup of up to two orders of magnitude relative to a similar tool using predicate abstraction. 1 ..."
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Cited by 75 (6 self)
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Abstract. We describe a model checker for infinitestate sequential programs, based on Craig interpolation and the lazy abstraction paradigm. On device driver benchmarks, we observe a speedup of up to two orders of magnitude relative to a similar tool using predicate abstraction. 1
A practical and complete approach to predicate refinement
 In Tools and Algorithms for the Construction and Analysis of Systems, LNCS 3920
, 2006
"... Abstract. Predicate abstraction is a method of synthesizing the strongest inductive invariant of a system expressible as a Boolean combination of a given set of atomic predicates. A predicate selection method can be said to be complete for a given theory if it is guaranteed to eventually find atomic ..."
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Cited by 55 (6 self)
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Abstract. Predicate abstraction is a method of synthesizing the strongest inductive invariant of a system expressible as a Boolean combination of a given set of atomic predicates. A predicate selection method can be said to be complete for a given theory if it is guaranteed to eventually find atomic predicates sufficient to prove a given property, when such exist. Current heuristics are incomplete, and often diverge on simple examples. We present a practical method of predicate selection that is complete in the above sense. The method is based on interpolation and uses a “split prover”, somewhat in the style of structurebased provers used in artificial intelligence. We show that it allows the verification of a variety of simple programs that cannot be verified by existing software model checkers. 1
Interpolantbased transition relation approximation
 In CAV 05: ComputerAided Verification, LNCS 3576
, 2005
"... Abstract. In predicate abstraction, exact image computation is problematic, requiring in the worst case an exponential number of calls to a decision procedure. For this reason, software model checkers typically use a weak approximation of the image. This can result in a failure to prove a property, ..."
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Cited by 38 (3 self)
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Abstract. In predicate abstraction, exact image computation is problematic, requiring in the worst case an exponential number of calls to a decision procedure. For this reason, software model checkers typically use a weak approximation of the image. This can result in a failure to prove a property, even given an adequate set of predicates. We present an interpolantbased method for strengthening the abstract transition relation in case of such failures. This approach guarantees convergence given an adequate set of predicates, without requiring an exact image computation. We show empirically that the method converges more rapidly than an earlier method based on counterexample analysis. 1
FRAIGs: A unifying representation for logic synthesis and verification
, 2005
"... ANDINV graphs (AIGs) are Boolean networks composed of twoinput ANDgates and inverters. In the known applications, such as equivalence checking and technology mapping, AIGs are used to represent and manipulate Boolean functions. AIGs powered by simulation and Boolean satisfiability lead to function ..."
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Cited by 37 (10 self)
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ANDINV graphs (AIGs) are Boolean networks composed of twoinput ANDgates and inverters. In the known applications, such as equivalence checking and technology mapping, AIGs are used to represent and manipulate Boolean functions. AIGs powered by simulation and Boolean satisfiability lead to functionally reduced AIGs (FRAIGs), which are “semicanonical ” in the sense that each FRAIG node has unique functionality among all the nodes currently present in the FRAIG. The paper shows that FRAIGs can be used to unify and enhance many phases of logic synthesis: from the representation of the original and the intermediate netlists derived by logic optimization, through technology mapping over multiple logic structures, to combinational equivalence checking. Experimental results on large public benchmarks confirm the practicality of using FRAIGs throughout the logic synthesis flow. 1
Array abstractions from proofs
 CAV, volume 4590 of LNCS
, 2007
"... Abstract. We present a technique for using infeasible program paths to automatically infer Range Predicates that describe properties of unbounded array segments. First, we build proofs showing the infeasibility of the paths, using axioms that precisely encode the highlevel (but informal) rules with ..."
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Cited by 33 (3 self)
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Abstract. We present a technique for using infeasible program paths to automatically infer Range Predicates that describe properties of unbounded array segments. First, we build proofs showing the infeasibility of the paths, using axioms that precisely encode the highlevel (but informal) rules with which programmers reason about arrays. Next, we mine the proofs for Craig Interpolants which correspond to predicates that refute the particular counterexample path. By embedding the predicate inference technique within a CounterexampleGuided AbstractionRefinement (CEGAR) loop, we obtain a method for verifying datasensitive safety properties whose precision is tailored in a program and propertysensitive manner. Though the axioms used are simple, we show that the method suffices to prove a variety of arraymanipulating programs that were previously beyond automatic model checkers. 1
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 32 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
On Computing Minimum Unsatisfiable Cores
, 2003
"... Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given a ..."
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Cited by 31 (3 self)
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Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given a
Compositional MayMust Program Analysis: Unleashing the Power of Alternation
"... Program analysis tools typically compute two types of information: (1) may information that is true of all program executions and is used to prove the absence of bugs in the program, and (2) must information that is true of some program executions and is used to prove the existence of bugs in the pr ..."
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Cited by 29 (9 self)
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Program analysis tools typically compute two types of information: (1) may information that is true of all program executions and is used to prove the absence of bugs in the program, and (2) must information that is true of some program executions and is used to prove the existence of bugs in the program. In this paper, we propose a new algorithm, dubbed SMASH, which computes both may and must information compositionally. At each procedure boundary, may and must information is represented and stored as may and must summaries, respectively. Those summaries are computed in a demanddriven manner and possibly using summaries of the opposite type. We have implemented SMASH using predicate abstraction (as in SLAM) for the may part and using dynamic test generation (as in DART) for the must part. Results of experiments with 69 Microsoft Windows Vista device drivers show that SMASH can significantly outperform mayonly, mustonly and noncompositional maymust algorithms. Indeed, our empirical results indicate that most complex code fragments in large programs are actually often either easy to prove irrelevant to the specific property of interest using may analysis or easy to traverse using directed testing. The finegrained coupling and alternation of may (universal) and must (existential) summaries allows SMASH to easily navigate through these code fragments while traditional mayonly, mustonly or noncompositional maymust algorithms are stuck in their specific analyses. 1.
INTERPOLATION IN LOCAL THEORY EXTENSIONS
, 2008
"... In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the base theory as blackboxes. We present several examples of t ..."
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Cited by 27 (15 self)
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In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the base theory as blackboxes. We present several examples of theory extensions in which interpolants can be computed this way, and discuss applications in verification, knowledge representation, and modular reasoning in combinations of local theories.