Efficient Computation of Answer Sets via SAT Modulo Acyclicity and Vertex Elimination

Answer set programming (ASP) is a declarative programming paradigm where the solutions of a search problem are captured by the answer sets of a logic program describing its solutions. Besides native algorithms implemented as answer-set solvers, the computation of answer sets can be realized (i) by translating the logic program into propositional logic or its extensions and (ii) by finding satisfying assignments with appropriate solvers. In this work, we recall the graph-based extension of propositional logic, viz. SAT modulo graphs, and the case of acyclicity constraint which keeps a digraph associated with each truth assignment acyclic. This particular extension lends itself very well for answer set computation, e.g., using extended SAT solvers, such as GRAPHSAT, as back-end solvers. The goal of this work, however, is to translate away the acyclicity extension altogether using a vertex elimination technique, giving rise to a translation from ASP into propositional clauses only. We use non-tight benchmarks and a state-of-the-art SAT solver, KISSAT, to illustrate that performance obtained in this way can be competitive against GRAPHSAT and native ASP solvers such as CLASP and WASP.