The Good, the Bad, and the Odd: Cycles in Answer-Set Programs
This work addresses computational complexity issues in answer-set programming, an incremental advancement in logic-based AI.
The paper tackles the problem of generalizing target classes for backdoors in answer-set programs by considering the parity of negative edges on cycles, establishing new hardness results and non-uniform polynomial-time tractability relative to cycles.
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.