Abstract. We describe the conflict-driven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1

Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, cross-fertilising 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 black-box 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

Abstract. Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proof-producing SMT (Satisfiability Modulo Theories) solver that contains a SAT engine and a decision procedure for quantifier-free first-order logic with equality. As a result, a user benefits from the expressiveness of Isabelle/HOL when modeling a system, but obtains much better automation for those fragments of the proofs that fall within the scope of the (automatic) SMT solver. Soundness is not compromised because all proofs are submitted to the trusted kernel of Isabelle for certification. This architecture is straightforward to extend for other interactive proof assistants and proof-producing reasoners. 1

We elaborate upon a recently proposed approach to finding an answer set of a logic program based on concepts from constraint processing and satisfiability checking. We extend this approach and propose a new algorithm for enumerating answer sets. The algorithm, which to our knowledge is novel even in the context of satisfiability checking, is implemented in the clasp answer set solver. We contrast our new approach to alternative systems and different options of clasp, and provide an empirical evaluation.

Abstract. Many real-world problems require the enumeration of all solutions of combinatorial search problems, even though this is often infeasible in practice. However, not always all parts of a solution are needed. We are thus interested in projecting solutions to a restricted vocabulary. Yet, the adaption of Boolean constraint solving algorithms turns out to be non-obvious provided one wants a repetition-free enumeration in polynomial space. We address this problem and propose a new algorithm computing projective solutions. Although we have implemented our approach in the context of Answer Set Programming, it is readily applicable to any solver based on modern Boolean constraint technology. 1

Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their long-term goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of high-level specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the so-called guarded fragments. In the case of k-guarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between k-guarded formulas and tree decompositions. 1

Abstract. Generic SAT solvers have been very successful in solving hard combinatorial problems in various application areas, including AI planning. There is potential for improved performance by making the SAT solving process more application-specific. In this paper we propose a variable selection strategy for AI planning. The strategy is based on generic principles about properties of plans, and its performance with standard planning benchmarks often substantially improves on generic variable selection heuristics used in SAT solving, such as the VSIDS strategy. These improvements lift the efficiency of SAT based planning to the same level as best planners that use other search methods. 1

We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be decomposed into logic programs such that unit-propagation achieves arc, bound or range consistency. Experiments with our encodings demonstrate their computational impact.

The attractiveness of Answer Set Programming (ASP) and related paradigms for declarative problem solving is considerably due to the availability of highly efficient yet easy-to-use implementations. A major driving force for the development and improvement of tools are standardized problem representations, for several reasons. First, they relieve developers from the burden of inventing their own input formats. Second, they establish interoperability between separate tools, allowing users to easily compare and exchange them without extensively converting their problem representations. Third, they facilitate the acquisition of problem descriptions from distinct sources, which is useful for benchmarking and assessment purposes. Historically, however, standards for representing logic programs, serving as inputs to ASP systems, were mainly dictated by the few available tools. In fact, there currently are two quasi standards, namely, the formats used by lparse and dlv, incompatible with each other. As a first step towards overcoming this deficiency, this work proposes an intermediate format for ground logic programs, intended for the representation of inputs to ASP solvers. The format is not designed to be a primary input language, given that ASP systems usually deploy a second component, called a grounder, to deal with the inputs provided by users. In view of this, our format is situated intermediate a grounder and a solver, guided by the example of grounder lparse and solver smodels, the latter marking the first among nowadays a variety of solvers processing the output of lparse. However, the output format of lparse has some decisive drawbacks, namely, its restrictive range and limited extensibility. We thus propose a new intermediate language, where our major design goals are flexibility in problem representation and easy extensibility to new language constructs.

Computational Grids provide a widely distributed computing environment suitable for randomized SAT solving. This paper develops techniques for incorporating clause learning, known to yield significant speed-ups in the sequential case, in such a distributed framework. The approach exploits existing state-of-the-art clause learning SAT solvers by embedding them with virtually no modifications. The paper presents an algorithmic framework for learning-enhanced randomized SAT solving in Grid environments. With a substantial amount of controlled experiments it is demonstrated that this approach enables a form of clause learning which is not directly available in the underlying sequential SAT solver. Finally, an implementation of the algorithm is run in a production level Grid where it solves several problems not solved in the SAT 2007 solver competition.