Polynomial-length planning spans the polynomial hierarchy

This paper presents a family of results on the computational complexity of planning: classical, conformant, and conditional with full or partial observability. Attention is restricted to plans of polynomially-bounded length. For conditional planning, restriction to plans of polynomial size is also considered. For this analysis, a planning domain is described by a transition relation encoded in classical propositional logic. Given the widespread use of satisfiability-based planning methods, this is a rather natural choice. Moreover, this allows us to develop a unified representation—in second-order propositional logic—of the range of planning problems considered. By describing a wide range of results within a single framework, the paper sheds new light on how planning complexity is affected by common assumptions such as nonconcurrency, determinism and polynomial-time decidability of executability of actions.