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

Abstract. Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in order to adapt them to the disjunctive case and demonstrate their implementation based on system CMODELS. 1

In this work we present a backjumping technique for Disjunctive Logic Programming under the Stable Model Semantics (SDLP). It builds upon related techniques that had originally been introduced for constraint solving, which have been adapted to propositional satisfiability testing, and recently also to non-disjunctive logic programming under the stable model semantics (SLP) [1, 2]. We focus on backjumping without clause learning, providing a new theoretical framework for backjumping in SDLP, elaborating on and exploiting peculiarities of the disjunctive setting. We present a reason calculus and associated computations, which – compared to the traditional approaches – reduces the information to be stored, while fully preserving the correctness and the efficiency of the backjumping technique, handling specific aspects of disjunction in a benign way. We implemented the proposed technique in DLV, the state-of-the-art SDLP system. We have conducted several experiments on hard random and structured instances in order to assess the impact of backjumping, using DLV with and without the backjumping method described in this paper, using as a parameter to both two different heuristic functions. Our

We elaborate a uniform approach to computing answer sets of disjunctive logic programs based on state-of-theart Boolean constraint solving techniques. Starting from a constraint-based characterization of answer sets, we develop advanced solving algorithms, featuring backjumping and conflict-driven learning using the First-UIP scheme as well as sophisticated unfounded set checking. As a final result, we obtain a competitive solver for Σ P 2-complete problems, taking advantage of Boolean constraint solving technology without using any legacy solvers as black boxes.

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. Answer Set Programming (ASP) is a declarative paradigm for solving search problems. State-of-the-art systems for ASP include SMODELS, DLV, CMODELS, and ASSAT. In this paper, our goal is to study the computational properties of such systems both from a theoretical and an experimental point of view. From the theoretical point of view, we start our analysis with CMODELS and SMODELS. We show that though these two systems are apparently different, they are equivalent on a significant class of programs, called tight. By equivalent, we mean that they explore search trees with the same branching nodes, (assuming, of course, a same branching heuristic). Given our result and that the CMODELS search engine is based on the Davis Logemann Loveland procedure (DLL) for propositional satisfiability (SAT), we are able to establish that many of the properties holding for DLL also hold for CMODELS and thus for SMODELS. On the other hand, we also show that there exist classes of non-tight programs which are exponentially hard for CMOD-ELS, but “easy ” for SMODELS. We also discuss how our results extend to other

Abstract. The PLATYPUS approach offers a generic platform for distributed answer set solving, accommodating a variety of different architectures for distributing the search for answer sets across different processes and different search modes for modifying search behaviour. We describe two major extensions of PLATYPUS. First, we present its probing mode which provides a controlled non-linear traversal of the search space. Second, we present its new multithreading architecture allowing for intra-process distribution. Both contributions are underpinned by experimental results illustrating their computational impact. 1

Competitive native solvers for Answer Set Programming (ASP) perform a backtracking search by assuming the truth of literals. The choice of literals (the heuristic) is fundamental for the performance of these systems. Most of the efficient ASP systems employ a heuristic based on look-ahead, that is, a literal is tentatively assumed and its heuristic value is based on its deterministic consequences. However, looking ahead is a costly operation, and indeed lookahead often accounts for the majority of time taken by ASP solvers. For Satisfiability (SAT), a radically different approach, called look-back heuristic, proved to be quite successful: Instead of looking ahead, one uses information gathered during the computation performed so far, thus looking back. In this approach, atoms which have been frequently involved in inconsistencies are preferred. In this paper, we carry over this approach to the framework of disjunctive ASP. We design a number of look-back heuristics exploiting peculiarities of ASP and implement them in the ASP system DLV. We compare their performance on a collection of hard ASP programs both structured and randomly generated. These experiments indicate that a very basic approach works well, outperforming all of the prominent disjunctive ASP systems — DLV (with its traditional heuristic), GnT, and CModels3 — on many of the instances considered.

Abstract. We propose an approach to distributed Answer Set Solving based on Message Passing. Our approach aims at taking advantage of modern ASP solvers rather than proposing a genuine yet involved parallel ASP solver. To this end, we rely upon a simple master-worker architecture in which each worker amounts to an off-the-shelf ASP solver augmented with a separate communication module being only lightly connected to the actual solver. The overall communication is driven by the workers ’ communication modules, which asynchronously exchange messages with the master. We have implemented our approach and report upon an empirical study demonstrating its computational impact. 1

Abstract. We investigate techniques for supporting inductive definitions (IDs) in SAT, and report on an implementation, called MidL, of the resulting solver. This solver was first introduced in [11], as a part of a declarative problem solving framework. We go about our investigation by proposing a new formulation of the semantics of IDs as presented in [2]. This new formulation suggests a way to perform the computational task involved, resulting in an algorithm supporting IDs. We show in detail how to integrate our algorithm with traditional SAT solving techniques. We also point out the similarities with another algorithm that was recently developed for ASP [1]. Indeed, our formulation reveals a very tight relation with stable model semantics. We conclude by an experimental validation of our approach using MidL. 1