Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
A polynomial algorithm for the parity path problem on perfectly orientable graphs
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
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
Pfaffian Orientations, 0/1 Permanents, and Even Cycles in Directed Graphs
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Finding Even Cycles Even Faster
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
On odd and even cycles in normal logic programs
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Backdoors to tractable answer-set programming
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Parameterized Complexity
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Backdoors of answer-set programs are sets of atoms that represent "clever reasoning shortcuts" through the search space. Assignments to backdoor atoms reduce the given program to several programs that belong to a tractable target class. Previous research has considered target classes based on notions of acyclicity where various types of cycles (good and bad cycles) are excluded from graph representations of programs. We generalize the target classes by taking the parity of the number of negative edges on bad cycles into account and consider backdoors for such classes. We establish new hardness results and non-uniform polynomial-time tractability relative to directed or undirected cycles.