ASSAT: computing answer sets of a logic program by SAT solvers

We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the programʹs completion, we obtain a one-to -one correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implement a system called ASSAT(X), depending on the SAT solver X used, for computing one answer set of a normal logic program with constraints. We test the system on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. Our experimental results show that in these domains, for the task of generating one answer set of a normal logic program, our system has a clear edge over the state-of-art answer set programming systems Smodels and DLV.