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43
Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT
, 2002
"... In this paper, we study the approach of dynamic local search for the SAT problem. We focus on the recent and promising Exponentiated SubGradient (ESG) algorithm, and examine the factors determining the time complexity of its search steps. Based on the insights gained from our analysis, we developed ..."
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Cited by 93 (21 self)
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In this paper, we study the approach of dynamic local search for the SAT problem. We focus on the recent and promising Exponentiated SubGradient (ESG) algorithm, and examine the factors determining the time complexity of its search steps. Based on the insights gained from our analysis, we developed Scaling and Probabilistic Smoothing (SAPS), an efficient SAT algorithm that is conceptually closely related to ESG. We also introduce a reactive version of SAPS (RSAPS) that adaptively tunes one of the algorithm's important parameters. We show that for a broad range of standard benchmark problems for SAT, SAPS and RSAPS achieve significantly better performance than both ESG and the stateoftheart WalkSAT variant, Novelty.
Watched literals for constraint propagation in minion
 In Proc. CP2006, 182–197
, 2006
"... Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three im ..."
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Cited by 39 (15 self)
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Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three important aspects of watched literals as we apply them to constraints, and we describe how they are implemented in the Minion constraint solver. We show three successful applications of watched literals to constraint propagators: the sum of boolean variables; generalised arc consistency for the ‘element ’ constraint; and generalised arc consistency for the ‘table ’ constraint. 1
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 37 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
A new approach to model counting
 In 8th SAT, volume 3569 of LNCS
, 2005
"... Abstract. We introduce ApproxCount, an algorithm that approximates the number of satisfying assignments or models of a formula in propositional logic. Many AI tasks, such as calculating degree of belief and reasoning in Bayesian networks, are computationally equivalent to model counting. It has been ..."
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Cited by 29 (7 self)
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Abstract. We introduce ApproxCount, an algorithm that approximates the number of satisfying assignments or models of a formula in propositional logic. Many AI tasks, such as calculating degree of belief and reasoning in Bayesian networks, are computationally equivalent to model counting. It has been shown that model counting in even the most restrictive logics, such as Horn logic, monotone CNF and 2CNF, is intractable in the worstcase. Moreover, even approximate model counting remains a worstcase intractable problem. So far, most practical model counting algorithms are based on backtrack style algorithms such as the DPLL procedure. These algorithms typically yield exact counts but are limited to relatively small formulas. Our ApproxCount algorithm is based on SampleSat, a new algorithm that samples from the solution space of a propositional logic formula nearuniformly. We provide experimental results for formulas from a variety of domains. The algorithm produces good estimates for formulas much larger than those that can be handled by existing algorithms. 1
MUP: A Minimal Unsatisfiability Prover
, 2005
"... After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the ext ..."
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Cited by 25 (0 self)
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After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the minimality of the results. This paper describes a practical algorithm that decides the minimal unsatisfiability of any CNF formula through BDD manipulation. This algorithm has a worsecase complexity that is exponential only in the treewidth of the CNF formula. We provide an empirical evaluation of the algorithm, highlighting its efficiency on a set of hard problems as well as its ability to work with existing subformula extraction tools to achieve optimal results.
Efficient Monte Carlo simulation via the generalized splitting method. Statistics and Computing
, 2011
"... We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide ..."
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Cited by 23 (8 self)
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We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rareevent probability estimation, counting, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy.
DPLL with a trace: From SAT to knowledge compilation
 IJCAI05
, 2005
"... We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of dDNNF, FBDD, and OBDD, respectively. These languages are decreasingly s ..."
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Cited by 22 (2 self)
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We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of dDNNF, FBDD, and OBDD, respectively. These languages are decreasingly succinct, yet increasingly tractable, supporting such polynomialtime queries as model counting and equivalence testing. Our contribution is thus twofold. First, we provide a uniform framework, supported by empirical evaluations, for compiling knowledge into various languages of interest. Second, we show that given a particular variant of DPLL, by identifying the language membership of its traces, one gains a fundamental understanding of the intrinsic complexity and computational power of the search algorithm itself. As interesting examples, we unveil the “hidden power” of several recent model counters, point to one of their potential limitations, and identify a key limitation of DPLLbased procedures in general.
Learning dynamic algorithm portfolios
 ANN MATH ARTIF INTELL (2006) 47:295–328
, 2006
"... Algorithm selection can be performed using a model of runtime distribution, learned during a preliminary training phase. There is a tradeoff between the performance of modelbased algorithm selection, and the cost of learning the model. In this paper, we treat this tradeoff in the context of bandi ..."
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Cited by 20 (1 self)
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Algorithm selection can be performed using a model of runtime distribution, learned during a preliminary training phase. There is a tradeoff between the performance of modelbased algorithm selection, and the cost of learning the model. In this paper, we treat this tradeoff in the context of bandit problems. We propose a fully dynamic and online algorithm selection technique, with no separate training phase: all candidate algorithms are run in parallel, while a model incrementally learns their runtime distributions. A redundant set of time allocators uses the partially trained model to propose machine time shares for the algorithms. A bandit problem solver mixes the modelbased shares with a uniform share, gradually increasing the impact of the best time allocators as the model improves. We present experiments with a set of SAT solvers on a mixed SATUNSAT benchmark; and with a set of solvers for the Auction Winner Determination problem.
The ILTP problem library for intuitionistic logic, release v1.1
 Journal of Automated Reasoning
"... Abstract. The Intuitionistic Logic Theorem Proving (ILTP) library provides a platform for testing and benchmarking automated theorem proving (ATP) systems for propositional and firstorder intuitionistic logic. It includes about 2800 problems in a standardized syntax from 24 problem domains collecte ..."
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Cited by 16 (5 self)
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Abstract. The Intuitionistic Logic Theorem Proving (ILTP) library provides a platform for testing and benchmarking automated theorem proving (ATP) systems for propositional and firstorder intuitionistic logic. It includes about 2800 problems in a standardized syntax from 24 problem domains collected from various sources that are appropriate for intuitionistic logic. For each problem intuitionistic status and difficulty rating were obtained by running comprehensive tests of currently available intuitionistic ATP systems on all problems in the library. Thus for the first time the testing and evaluation of intuitionistic ATP systems is put onto a firm basis. Keywords: ILTP, problem library, benchmarking, experimental evaluation, ATP, intuitionistic logic
Using DPLL for efficient OBDD construction
 In Seventh International Conference on Theory and Applications of Satisfiability Testing, SAT 2004, Revised Selected Papers
, 2004
"... Abstract. The DPLL procedure has found great success in SAT, where search terminates on the first solution discovered. We show that this procedure is equally promising in a problem where exhaustive search is used, given that it is augmented with appropriate caching. Specifically, we propose two DPLL ..."
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Cited by 16 (4 self)
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Abstract. The DPLL procedure has found great success in SAT, where search terminates on the first solution discovered. We show that this procedure is equally promising in a problem where exhaustive search is used, given that it is augmented with appropriate caching. Specifically, we propose two DPLLbased algorithms that construct OBDDs for CNF formulas. These algorithms have a worstcase complexity that is linear in the number of variables and size of the CNF, and exponential only in the cutwidth or pathwidth of the variable ordering. We show how modern SAT techniques can be harnessed by implementing the algorithms on top of an existing SAT solver. We discuss the advantage of this new construction method over the traditional approach, where OBDDs for subsets of the CNF formula are built and conjoined. Our experiments indicate that on many CNF benchmarks, the new method runs orders of magnitude faster than a comparable implementation of the traditional method. 1