The Good, the Bad, and the Odd: Cycles in Answer-Set Programs

TL;DR

This paper explores the concept of backdoors in answer-set programming, focusing on cycles and their parity to identify tractable subclasses, and establishes new complexity results for these classes.

Contribution

It generalizes previous cycle-based target classes by incorporating cycle parity, providing new hardness and tractability results for backdoor detection.

Findings

New hardness results for cycle-based classes

Polynomial-time tractability for classes with cycle parity considerations

Extension of backdoor concepts to more complex cycle structures

Abstract

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.