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We present trichotomy results characterizing the complexity of reasoning withdisjunctive logic programs. To this end, we introduce a certain definitionschema for classes of programs based on a set of allowed arities of rules. Weshow that each such class of programs has a finite representation, and for eachof the classes definable in the schema we characterize the complexity of theexistence of an answer set problem. Next, we derive similar characterizationsof the complexity of skeptical and credulous reasoning with disjunctive logicprograms. Such results are of potential interest. On the one hand, they revealsome reasons responsible for the hardness of computing answer sets. On theother hand, they identify classes of problem instances, for which the problemis "easy" (in P) or "easier than in general" (in NP). We obtain similar resultsfor the complexity of reasoning with disjunctive programs under thesupported-model semantics. To appear in Theory and Practice of LogicProgramming (TPLP)

Trichotomy and Dichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs