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49
Stable Models and Circumscription
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (includ ..."
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Cited by 73 (39 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from John McCarthy’s definition of circumscription.
What Is Answer Set Programming?
, 2008
"... Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledgeintensive applications. ASP programs consist of rules tha ..."
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Cited by 64 (10 self)
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Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledgeintensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.
Satbased answer set programming
 In Proc. AAAI04
, 2004
"... The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either ..."
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Cited by 45 (12 self)
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The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a onetoone correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SATbased decision procedure for answer set programming that (i) deals with any (non disjunctive) logic program, (ii) works on a SAT formula without additional variables, and (iii) is guaranteed to work in polynomial space. Further, our procedure can be extended to compute all the answer sets still working in polynomial space. The experimental results of a prototypical implementation show that the approach can pay off sometimes by orders of magnitude.
Latent Class Models for Algorithm Portfolio Methods
"... Different solvers for computationally difficult problems such as satisfiability (SAT) perform best on different instances. Algorithm portfolios exploit this phenomenon by predicting solvers ’ performance on specific problem instances, then shifting computational resources to the solvers that appear ..."
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Cited by 15 (4 self)
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Different solvers for computationally difficult problems such as satisfiability (SAT) perform best on different instances. Algorithm portfolios exploit this phenomenon by predicting solvers ’ performance on specific problem instances, then shifting computational resources to the solvers that appear best suited. This paper develops a new approach to the problem of making such performance predictions: natural generative models of solver behavior. Two are proposed, both following from an assumption that problem instances cluster into latent classes: a mixture of multinomial distributions, and a mixture of Dirichlet compound multinomial distributions. The latter model extends the former to capture burstiness, the tendency of solver outcomes to recur. These models are integrated into an algorithm portfolio architecture and used to run standard SAT solvers on competition benchmarks. This approach is found competitive with the most prominent existing portfolio, SATzilla, which relies on domainspecific, handselected problem features; the latent class models, in contrast, use minimal domain knowledge. Their success suggests that these models can lead to more powerful and more general algorithm portfolio methods.
Backdoors to satisfaction
 The Multivariate Algorithmic Revolution and Beyond  Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday, volume 7370 of Lecture
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Advanced Preprocessing for Answer Set Solving
"... Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program ( ..."
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Cited by 12 (5 self)
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Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program (in terms of Boolean constraints). We implemented our approach as well as a SATbased technique to reduce Boolean constraints. This allows us to empirically analyze both preprocessing types and to demonstrate their computational impact. 1
Formalization and Implementation of Modern SAT Solvers
"... Most, if not all, stateoftheart complete SAT solvers are complex variations of the DPLL procedure described in the early 1960’s. Published descriptions of these modern algorithms and related data structures are given either as highlevel (rulebased) transition systems or, informally, as (pseudo) ..."
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Cited by 11 (1 self)
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Most, if not all, stateoftheart complete SAT solvers are complex variations of the DPLL procedure described in the early 1960’s. Published descriptions of these modern algorithms and related data structures are given either as highlevel (rulebased) transition systems or, informally, as (pseudo) programming language code. The former, although often accompanied with (informal) correctness proofs, are usually very abstract and do not specify many details crucial for efficient implementation. The latter usually do not involve any correctness argument and the given code is often hard to understand and modify. This paper aims at bridging this gap: we present SAT solving algorithms that are formally proved correct, but at the same time they contain information required for efficient implementation. We use a tutorial, topdown, approach and develop a SAT solver, starting from a simple design that is subsequently extended, stepbystep, with the requisite series of features. Heuristic parts of the solver are abstracted away, since they usually do not affect solver correctness (although they are very important for efficiency). All algorithms are given in pseudocode. The code is accompanied with correctness conditions, given in Hoare logic style. Correctness proofs are formalized within the Isabelle theorem proving system and are available in the extended version of this paper. The given pseudocode served as a basis for our SAT solver argosat.
InstanceBased Selection of Policies for SAT Solvers
, 2009
"... Execution of most of the modern DPLLbased SAT solvers is guided by a number of heuristics. Decisions made during the search process are usually driven by some fixed heuristic policies. Despite the outstanding progress in SAT solving in recent years, there is still an appealing lack of techniques f ..."
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Cited by 9 (1 self)
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Execution of most of the modern DPLLbased SAT solvers is guided by a number of heuristics. Decisions made during the search process are usually driven by some fixed heuristic policies. Despite the outstanding progress in SAT solving in recent years, there is still an appealing lack of techniques for selecting policies appropriate for solving specific input formulae. In this paper we present a methodology for instancebased selection of solver’s policies that uses a datamining classification technique. The methodology also relies on analysis of relationships between formulae, their families, and their suitable solving strategies. The evaluation results are very good, demonstrate practical usability of the methodology, and encourage further efforts in this direction.
Minimal Sets over Monotone Predicates in Boolean Formulae
"... Abstract. The importance and impact of the Boolean satisfiability (SAT) problem in many practical settings is wellknown. Besides SAT, a number of computational problems related with Boolean formulas find a wide range of practical applications. Concrete examples for CNF formulas include computing pr ..."
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Cited by 8 (4 self)
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Abstract. The importance and impact of the Boolean satisfiability (SAT) problem in many practical settings is wellknown. Besides SAT, a number of computational problems related with Boolean formulas find a wide range of practical applications. Concrete examples for CNF formulas include computing prime implicates (PIs), minimal models (MMs), minimal unsatisfiable subsets (MUSes), minimal equivalent subsets (MESes) and minimal correction subsets (MCSes), among several others. This paper builds on earlier work by Bradley and Manna and shows that all these computational problems can be viewed as computing a minimal set subject to a monotone predicate, i.e. the MSMP problem. Thus, if cast as instances of the MSMP problem, these computational problems can be solved with the same algorithms. More importantly, the insights provided by this result allow developing a new algorithm for the general MSMP problem, that is asymptotically optimal. Moreover, in contrast with other asymptotically optimal algorithms, the new algorithm performs competitively in practice. The paper carries out a comprehensive experimental evaluation of the new algorithm on the MUS problem, and demonstrates that it outperforms state of the art MUS extraction algorithms. 1
EWLS: A New Local Search for Minimum Vertex Cover
 PROCEEDINGS OF THE TWENTYFOURTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI10)
, 2010
"... A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on t ..."
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Cited by 7 (3 self)
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A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on the idea of extending a partial vertex cover into a vertex cover. A key point of EWLS is to find a vertex set that provides a tight upper bound on the size of the minimum vertex cover. To this purpose, EWLS employs an iterated local search procedure, using an edge weighting scheme which updates edge weights when stuck in local optima. Moreover, some sophisticated search strategies have been taken to improve the quality of local optima. Experimental results on the broadly used DIMACS benchmark show that EWLS is competitive with the current best heuristic algorithms, and outperforms them on hard instances. Furthermore, on a suite of difficult benchmarks, EWLS delivers the best results and sets a new record on the largest instance.