On the Structural Complexity of Grounding – Tackling the ASP Grounding Bottleneck via Epistemic Programs and Treewidth

Abstract

Answer Set Programming is widely applied research area for knowledge representation and for solving industrial domains. One of the challenges of this formalism focuses on the so-called grounding bottleneck, which addresses the efficient replacement of first-order variables by means of domain values. Recently, there have been several works in this direction, ranging from lazy grounding, hybrid solving, over translational approaches. Inspired by a translation from non-ground normal programs to ground disjunctive programs, we attack the grounding bottleneck from a more general angle. We provide a polynomial reduction for grounding disjunctive programs of bounded domain size by reducing to propositional epistemic logic programs (ELPs). By slightly adapting our reduction, we show new complexity results for non-ground programs that adhere to the measure treewidth. We complement these results by matching lower bounds under the exponential time hypothesis, ruling out significantly better algorithms.