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28
BerkMin: a fast and robust satsolver
, 2002
"... We describe a SATsolver, BerkMin, that inherits such features of GRASP, SATO, and Chaff as clause recording, fast BCP, restarts, and conflict clause “aging”. At the same time BerkMin introduces a new decision making procedure and a new method of clause database management. We experimentally compare ..."
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Cited by 275 (5 self)
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We describe a SATsolver, BerkMin, that inherits such features of GRASP, SATO, and Chaff as clause recording, fast BCP, restarts, and conflict clause “aging”. At the same time BerkMin introduces a new decision making procedure and a new method of clause database management. We experimentally compare BerkMin with Chaff, the leader among SATsolvers used in the EDA domain. Experiments show that our solver is more robust than Chaff. BerkMin solved all the instances we used in experiments including very large CNFs from a microprocessor verification benchmark suite. On the other hand, Chaff was not able to complete some instances even with the timeout limit of 16 hours. 1.
Using Randomization and Learning to Solve Hard RealWorld Instances of Satisfiability
, 2000
"... This paper addresses the interaction between randomization, with restart strategies, and learning, an often crucial technique for proving unsatisfiability. We use instances of SAT from the hardware verification domain to provide evidence that randomization can indeed be essential in solving realwor ..."
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Cited by 58 (18 self)
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This paper addresses the interaction between randomization, with restart strategies, and learning, an often crucial technique for proving unsatisfiability. We use instances of SAT from the hardware verification domain to provide evidence that randomization can indeed be essential in solving realworld satis able instances of SAT. More interestingly, our results indicate that randomized restarts and learning may cooperate in proving both satisfiability and unsatisfiability. Finally, we utilize and expand the idea of algorithm portfolio design to propose an alternative approach for solving hard unsatisfiable instances of SAT.
Boosting Verification by Automatic Tuning of Decision Procedures
 SEVENTH INTERNATIONAL CONFERENCE ON FORMAL METHODS IN COMPUTERAIDED DESIGN
, 2007
"... Parameterized heuristics abound in computer aided design and verification, and manual tuning of the respective parameters is difficult and timeconsuming. Very recent results from the artificial intelligence (AI) community suggest that this tuning process can be automated, and that doing so can lead ..."
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Cited by 58 (37 self)
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Parameterized heuristics abound in computer aided design and verification, and manual tuning of the respective parameters is difficult and timeconsuming. Very recent results from the artificial intelligence (AI) community suggest that this tuning process can be automated, and that doing so can lead to significant performance improvements; furthermore, automated parameter optimization can provide valuable guidance during the development of heuristic algorithms. In this paper, we study how such an AI approach can improve a stateoftheart SAT solver for large, realworld bounded modelchecking and software verification instances. The resulting, automaticallyderived parameter settings yielded runtimes on average 4.5 times faster on bounded model checking instances and 500 times faster on software verification problems than extensive handtuning of the decision procedure. Furthermore, the availability of automatic tuning influenced the design of the solver, and the automaticallyderived parameter settings provided a deeper insight into the properties of problem instances.
Tuning SAT checkers for Bounded Model Checking
, 2000
"... Bounded Model Checking based on SAT methods has recently been introduced as a complementary technique to BDDbased Symbolic Model Checking. The basic idea is to search for a counter example in executions whose length is bounded by some integer k. The BMC problem can be efficiently reduced to a p ..."
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Cited by 45 (1 self)
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Bounded Model Checking based on SAT methods has recently been introduced as a complementary technique to BDDbased Symbolic Model Checking. The basic idea is to search for a counter example in executions whose length is bounded by some integer k. The BMC problem can be efficiently reduced to a propositional satisfiability problem, and can therefore be solved by SAT methods rather than BDDs. SAT procedures are based on generalpurpose heuristics that are designed for any propositional formula. We show that the unique characteristics of BMC formulas can be exploited for a variety of optimizations in the SAT checking procedure. Experiments with these optimizations on real designs proved their efficiency in many of the hard test cases, comparing to both the standard SAT procedure and a BDDbased model checker.
Heuristics for fast exact model counting
 In Proc. 8th International Conference on Theory and Applications of Satisfiability Testing
, 2005
"... Abstract. An important extension of satisfiability testing is modelcounting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact modelcounting algorithm that combines formula caching, clause le ..."
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Cited by 31 (2 self)
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Abstract. An important extension of satisfiability testing is modelcounting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact modelcounting algorithm that combines formula caching, clause learning, and component analysis. This paper reports on experiments with various techniques for improving the performance of Cachet, including componentselection strategies, variableselection branching heuristics, randomization, backtracking schemes, and crosscomponent implications. The result of this work is a highlytuned version of Cachet, the first (and currently, only) system able to exactly determine the marginal probabilities of variables in random 3SAT formulas with 150+ variables. We use this to discover an interesting property of random formulas that does not seem to have been previously observed. 1
Abstraction Refinement for Bounded Model Checking
 In Proc. CAV’05
, 2005
"... have been very successful in model checking large systems. While most previous work has focused on model checking, this paper presents a CounterexampleGuided abstraction refinement technique for Bounded Model Checking (bmc). Our technique makes bmc much faster, as indicated by our experiments. bmc ..."
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Cited by 15 (2 self)
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have been very successful in model checking large systems. While most previous work has focused on model checking, this paper presents a CounterexampleGuided abstraction refinement technique for Bounded Model Checking (bmc). Our technique makes bmc much faster, as indicated by our experiments. bmc is also used for generating refinements in the ProofBased Refinement (pbr) framework. We show that our technique unifies pbr and cegar into an abstractionrefinement framework that can balance the model checking and refinement efforts. 1
CirCUs: A hybrid satisfiability solver
 In International Conference on Theory and Applications of Satisfiability Testing (SAT 2004
, 2004
"... Abstract. CirCUs is a satisfiability solver that works on a combination of an AndInverterGraph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are ..."
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Cited by 13 (3 self)
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Abstract. CirCUs is a satisfiability solver that works on a combination of an AndInverterGraph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are sorted by solving a hypergraph linear arrangement problem. Then they are clustered by an algorithm that strives to avoid explosion in the resulting BDD sizes. If clustering results in a single diagram, the SAT instance is solved directly. Otherwise, search for a satisfying assignment is conducted on the original clauses, enhanced with information extracted from the BDDs. We also describe a new decision variable selection heuristic that is based on recognizing that the variables involved in a conflict clause are often best treated as a related group. We present experimental results that demonstrate CirCUs’s efficiency especially for mediumsize SAT instances that are hard to solve by traditional solvers based on DPLL. 1
Learning Abstractions for Model Checking
, 2006
"... not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: abstraction, boolean satisfiability, bounded model checking, broken trace, decision tree, formal methods, integer linear programmin ..."
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Cited by 12 (0 self)
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not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: abstraction, boolean satisfiability, bounded model checking, broken trace, decision tree, formal methods, integer linear programming, machine learning, Learning is a process that causes a system to improve its performance through experience. Inductive learning is the process of learning by examples, i.e. the system learns a general rule from a set of sample instances. Abstraction techniques have been successful in model checking large systems by enabling the model checker to ignore irrelevant details. The aim of abstraction is to identify a small abstract model on which the property holds. Most previous approaches for automatically generating abstract models are based on heuristics combined with the iterative abstractionrefinement loop. These techniques provide no guarantees on the size of the abstract models.
The Interplay of Randomization and Learning on RealWorld Instances of Satisfiability
, 2000
"... Recent work on the Satisfiability Problem (SAT) has provided strong empirical and theoretical evidence of the advantages of applying randomization and restarts in solving satisfiable problem instances. This paper addresses the interaction between randomization, with restart strategies, and learning, ..."
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Cited by 8 (1 self)
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Recent work on the Satisfiability Problem (SAT) has provided strong empirical and theoretical evidence of the advantages of applying randomization and restarts in solving satisfiable problem instances. This paper addresses the interaction between randomization, with restart strategies, and learning, an often crucial technique for proving unsatisfiability. We use instances of SAT from the hardware verification domain to provide evidence that randomization can indeed be essential in solving realworld satis able instances of SAT. More interestingly, our results indicate that randomized restarts and learning may cooperate in proving both satisfiability and unsatisfiability. Finally, we utilize and expand the idea of algorithm portfolio design to propose an alternative approach for solving hard unsatisfiable instances of SAT.
Refining the SAT Decision Ordering for Bounded Model Checking
, 2004
"... Bounded Model Checking (BMC) relies on solving a sequence of highly correlated Boolean satisfiability (SAT) problems, each of which corresponds to the existence of counterexamples of a bounded length. These satisfiability problems are usually decided by SAT solvers, whose performance depends heavil ..."
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Cited by 7 (1 self)
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Bounded Model Checking (BMC) relies on solving a sequence of highly correlated Boolean satisfiability (SAT) problems, each of which corresponds to the existence of counterexamples of a bounded length. These satisfiability problems are usually decided by SAT solvers, whose performance depends heavily on the variable decision ordering. The satisfiability problems in BMC have some unique characteristics that can be used to help the SAT decision making, but so far they have not been explored by the decision heuristics of most modern SAT solvers. We propose an algorithm to exploit the correlation among the sequence of SAT problems in BMC, by predicting and successively refining a partial variable ordering. This variable ordering is computed based on the analysis of all previous unsatisfiable instances, and is then combined with the SAT solver’s existing decision heuristic to determine the final variable decision ordering. Experiments on real designs from industry showed that our new method improved the performance of SATbased BMC significantly.