Computing Loops with at Most One External Support Rule for Disjunctive Logic Programs

We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constraints, an iterative procedure based on these formulas, the program completion, and unit propagation computes the least fixed point of a simplification operator used by DLV. We also relate loops with no external supports to the unfounded sets and the well-founded semantics of disjunctive logic programs by Wang and Zhou. However, the problem of computing loop formulas of loops with at most one external support rule is NP-hard for disjunctive logic programs. We thus propose a polynomial algorithm for computing some of these loop formulas, and show experimentally that this polynomial approximation algorithm can be effective in practice.