Backdoors to Tractability of Answer-Set Programming

Abstract

The practical results of answer-set programming indicate that classical complexity theory is insufficient as a theoretical framework to explain why modern answer-set programming solvers work fast on industrial applications. Complexity analysis by means of parameterized complexity theory seems to be promising, because we think that the reason for the gap between theory and practice is the presence of a "hidden structure" in real-world instances. The application of parameterized complexity theory to answer-set programming would give a crucial understanding of how solver heuristics work. This profound understanding can be used to improve the decision heuristics of modern solvers and yields new efficient algorithms for decision problems in the nonmonotonic setting. My research aims to explain the gap between theoretical upper bounds and the effort to solve real-world instances. I will further develop by means of parameterized complexity exact algorithms which work efficiently for real-world instances. The approach is based on backdoors which are small sets of atoms that represent "clever reasoning shortcuts" through the search space. The concept of backdoors is widely used in the areas of propositional satisfiability and constraint satisfaction. I will show how this concept can be adapted to the nonmonotonic setting and how it can be utilized to improve common algorithms.