On the Compilability of Bounded Numeric Planning

Bounded numeric planning, where each numeric variable domain is bounded, is PSPACE-complete, but such a complexity result does not capture how hard it really is, since the same holds even for the practically much easier STRIPS fragment. A finer way to compare the difficulty of planning formalisms is through the notion of compilability, which has been however extensively studied only for classical planning by Nebel. This paper extends Nebel's framework to the setting of bounded numeric planning. First, we identify a variety of numeric fragments differing on the degree of the polynomials involved and the availability of features such as conditional effects and Boolean conditions; then we study the compilability of these fragments to each other and to the classical fragments. Surprisingly, numeric and classical planning with conditional effects and Boolean conditions can be compiled both ways preserving plan size exactly, while the same does not hold when targeting pure STRIPS. Our study reveals also that numeric fragments cluster into two equivalence classes separated by the availability of incomplete initial state specifications, a feature allowing to specify uncertainty in the initial state.