Complexity, Decidability and Undecidability Results for Domain-Independent Planning

In this paper, we examine how the complexity of domain-independent planning with STRIPS-style 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 [5], and clear up some difficulties with his undecidability theorems. For those cases where planning is decidable, we explain 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. • whether or not the operators can have conditional effects. ? This work was supported in part by the Army Research Office under Grant Number DAAL-03-92-G-0225, by the Air Force Office of Scientific Research under grant F49620-93-1-0065, by an NSF Young Investigator Award IRI-93-57756, as well as by NSF Grant NSFD CDR-88003012 to the University of Maryland Systems Research Center, and NSF grants IRI-8907890 and IRI-9109755.