In this paper, we examine how the complexity of domain- independent planning with STRIPS-like operators depends on the nature of the planning operators.

We show conditions under which planning is decidable and undecidable. Our results on this topic solve an open problem posed by Chapman [4], and clear up some difficulties with his undecidability theorems.

For those cases where planning is decidable, we show how the time complexity varies depending on a wide variety of conditions:  whether or not function symbols are allowed; whether or not delete lists are allowed; whether or not negative preconditions are allowed; whether or not the predicates are restricted to be propositional (i.e., 0-ary); whether the planning operators are given as part of the input to the planning problem, or instead are fixed in advance.