Adapting techniques from database theory in order to optimize Answer Set
Programming (ASP) systems, and in particular the grounding components of ASP
systems, is an important topic in ASP. In recent years, the Magic Set method
has received some interest in this setting, and a variant of it, called DMS,
has been proposed for ASP. However, this technique has a caveat, because it is
not correct (in the sense of being query-equivalent) for all ASP programs. In
recent work, a large fragment of ASP programs, referred to as super-coherent
programs, has been identified, for which DMS is correct. The fragment contains
all programs which possess at least one answer set, no matter which set of
facts is added to them. Two open question remained: How complex is it to
determine whether a given program is super-coherent? Does the restriction to
super-coherent programs limit the problems that can be solved? Especially the
first question turned out to be quite difficult to answer precisely. In this
paper, we formally prove that deciding whether a propositional program is
super-coherent is \Pi^P_3-complete in the disjunctive case, while it is
\Pi^P_2-complete for normal programs. The hardness proofs are the difficult
part in this endeavor: We proceed by characterizing the reductions by the
models and reduct models which the ASP programs should have, and then provide
instantiations that meet the given specifications. Concerning the second
question, we show that all relevant ASP reasoning tasks can be transformed into
tasks over super-coherent programs, even though this transformation is more of
theoretical than practical interest.
To appear in Theory and Practice of Logic Programming (TPLP).Comment: 22 pages, 1 figure, journal pape