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Dual-normal Logic Programs - the Forgotten Class
Disjunctive Answer Set Programming is a powerful declarative programming
paradigm with complexity beyond NP. Identifying classes of programs for which
the consistency problem is in NP is of interest from the theoretical standpoint
and can potentially lead to improvements in the design of answer set
programming solvers. One of such classes consists of dual-normal programs,
where the number of positive body atoms in proper rules is at most one. Unlike
other classes of programs, dual-normal programs have received little attention
so far. In this paper we study this class. We relate dual-normal programs to
propositional theories and to normal programs by presenting several
inter-translations. With the translation from dual-normal to normal programs at
hand, we introduce the novel class of body-cycle free programs, which are in
many respects dual to head-cycle free programs. We establish the expressive
power of dual-normal programs in terms of SE- and UE-models, and compare them
to normal programs. We also discuss the complexity of deciding whether
dual-normal programs are strongly and uniformly equivalent.Comment: This is the author's self-archived copy including detailed proofs. To
appear in Theory and Practice of Logic Programming (TPLP), Proceedings of the
31st International Conference on Logic Programming (ICLP 2015