Journal of the ACM (JACM)
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Testing the Equivalence of Logic Programs under Stable Model Semantics
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Bounded Model Construction for Monadic Second-Order Logics
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Solving #SAT using vertex covers
Acta Informatica
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Almost 2-SAT Is Fixed-Parameter Tractable (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
On odd and even cycles in normal logic programs
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
A hierarchy of tractable subsets for computing stable models
Journal of Artificial Intelligence Research
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Answer-set programming with bounded treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Subset feedback vertex set is fixed-parameter tractable
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Augmenting tractable fragments of abstract argumentation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Parameterized Complexity
Augmenting tractable fragments of abstract argumentation
Artificial Intelligence
Augmenting tractable fragments of abstract argumentation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The Multivariate Algorithmic Revolution and Beyond
The good, the bad, and the odd: cycles in answer-set programs
ESSLLI'10 Proceedings of the 2010 international conference on New Directions in Logic, Language and Computation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We present a unifying approach to the efficient evaluation of propositional answer-set programs. Our 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. We show how this concept can be adapted to the nonmonotonic setting and how it allows to augment various known tractable subproblems, such as the evaluation of Horn and acyclic programs. In order to use backdoors we need to find them first. We utilize recent advances in fixed-parameter algorithmics to detect small backdoors. This implies fixed-parameter tractability of the evaluation of propositional answer-set programs, parameterized by the size of backdoors. Hence backdoor size provides a structural parameter similar to the treewidth parameter previously considered. We show that backdoor size and treewidth are incomparable, hence there are instances that are hard for one and easy for the other parameter. We complement our theoretical results with first empirical results.