A Theoretical Study of Domain-Independent Planning∗

In two previous conference papers, we examined how the decidability (?) and complexity (?) of domainindependent planning with STRIPS-style planning operators depends on the nature of the operators. However, space constraints did not allow us to include much discussion of the meaning and significance of this work—and in addition, we have subsequently produced several additional results that did not appear in those papers. In this report, we briefly summarize both our previous and current results, and then concentrate on discussing their meaning, significance, and relation to others’ work. We discuss conditions under which planning is decidable and undecidable. Our results on this topic solve an open problem posed by Chapman (?), and clear up some difficulties with his undecidability theorems. For those cases where planning is decidable, we discuss how the time complexity varies depending on a wide variety of conditions: (1) whether or not function symbols are allowed; (2) whether or not delete lists are allowed; (3) whether or not negative preconditions are allowed; (4) whether or not the predicates are restricted to be propositional (i.e., 0-ary); and (5) whether the planning operators are given as part of the input to the planning problem, or instead are fixed in advance. Chapman (?) and Dean and Boddy (?) studied planning with conditional operators, and showed that the problem of deciding whether a proposition is necessarily true after a partially ordered plan (a.k.a modal truth criterion) is NP-hard in the presence of conditional operators. The same problem can be solved in polynomial time when conditional operators are not allowed, and this led researchers to believe that plan-