Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas.In this paper, we present a SAT-based procedure, called ASP-SAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASP-SAT. From a practical perspective, we have (i) implemented ASP-SAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on "small but hard" problems are ineffective on "big but easy" problems and vice versa.

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Abstract. When a logic program is processed by an answer set solver, the first task is to generate its instantiation. In a recent paper, Calimeri et el. made the idea of efficient instantiation precise for the case of disjunctive programs with function symbols, and introduced the class of "finitely ground" programs that can be efficiently instantiated. Since that class is undecidable, it is important to find its large decidable subsets. In this paper, we introduce such a subset-the class of argumentrestricted programs. It includes, in particular, all finite domain programs, ω-restricted programs, and λ-restricted programs.

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Nieuwenhuis et al. (2006. Solving SAT and SAT modulo theories: From an abstract DavisPutnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937977 showed how to describe enhancements of the Davis-Putnam-Logemann-Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for several algorithms that generate answer sets for logic programs: smodels, smodels cc , asp-sat with Learning (cmodels), and a newly designed and implemented algorithm sup. This approach to describe answer set solvers makes it easier to prove their correctness, to compare them, and to design new systems.

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Abstract. The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose the notion of head-elementary-set-free (HEF) programs, a more general class of disjunctive programs than head-cycle-free (HCF) programs proposed by Ben-Eliyahu and Dechter, that can still be turned into nondisjunctive programs in polynomial time and space by "shifting" the head atoms into the body. We show several properties of HEF programs that generalize earlier results on HCF programs. Given an HEF program, we provide an algorithm for finding an elementary set whose loop formula is not satisfied, which has a potential for improving stable model computation by answer set solvers.

A fundamental task for propositional logic is to compute models of propositional formulas. Programs developed for this task are called satisfiability solvers. We show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for solvers developed for two other propositional formalisms: logic programming under the answer-set semantics, and the logic PC(ID). We show that in each case the task of computing models can be seen as "satisfiability modulo answer-set programming," where the goal is to find a model of a theory that also is an answer set of a certain program. The unifying perspective we develop shows, in particular, that solvers clasp and minisat(id) are closely related despite being developed for different formalisms, one for answer-set programming and the latter for the logic PC(ID).