The impact of treewidth on ASP grounding and solving of Answer Set Programs

Peer reviewe

DynASP2.5: Dynamic Programming on Tree Decompositions in Action

Efficient, exact parameterized algorithms are a vibrant theoretical research area. Recent solving competitions, such as the PACE challenge, show that there is also increasing practical interest in the parameterized algorithms community. An important research question is whether such algorithms can be built to efficiently solve specific problems in practice, that is, to be competitive with established solving systems. In this paper, we consider Answer Set Programming (ASP), a logic-based declarative modeling and problem solving framework. State-of-the-art ASP solvers generally rely on SAT-based algorithms. In addition, DynASP2, an ASP solver that is based on a classical dynamic programming on tree decompositions, has recently been introduced. DynASP2 outperforms modern ASP solvers when the goal is to count the number of solutions of programs that have small treewidth. However, for quickly finding one solutions, DynASP2 proved uncompetitive. In this paper, we present a new algorithm and implementation, called DynASP2.5, that shows competitive behavior compared to state-of-the-art ASP solvers on problems like Steiner tree for low-treewidth graphs, even when the task is to find just one solution. Our implementation is based on a novel approach that we call multi-pass dynamic programming

Acyclic Query Answering under Guarded Disjunctive Existential Rules and Consequences to DLs

International audienceThe complete picture of the complexity of conjunctive query answer-ing under guarded disjunctive existential rules has been recently settled. However, in the case of (unions of) acyclic conjunctive queries ((U)ACQs) there are some fundamental questions which are still open. It is the precise aim of the present paper to close those questions, and to understand whether the acyclicity of the query has a positive impact on the complexity of query answering. Our main re-sult states that acyclic conjunctive query answering under a fixed set of guarded disjunctive existential rules is EXPTIME-hard. This result together with an EXP-TIME upper bound obtained by exploiting classical results on guarded first-order logic, gives us a complete picture of the complexity of our problem. We also show that our results can be used as a generic tool for establishing results on (U)ACQ answering under several central DLs. In fact, restricting the query lan-guage to UACQs improves the complexity to EXPTIME-complete for any DL between DL-Lite bool and ALCHI; this holds even for fixed TBoxes