On the Compilability and Expressive Power of Propositional Planning Formalisms

The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of ``expressive power'''' is. We formalize the intuition that expressive power is a measure of how concisely planning domains and plans can be expressed in a particular formalism by introducing the notion of ``compilation schemes'''' between planning formalisms. Such compilation schemes restrict the growth of planning domains and the corresponding plans. Using this notion, we analyze the expressiveness of a large family of propositional planning formalisms, ranging from basic STRIPS to a formalism with conditional effects, partial state specifications, and propositional formulae in the preconditions. One of the results is that conditional effects cannot be compiled away if plan size should grow only linearly but can be compiled away if we allow for polynomial growth of the resulting plans. This result confirms that the recently proposed extensions to the GRAPHPLAN algorithm concerning conditional effects are optimal with respect to the ``compilability'''' framework. Another result is that general propositional formulae cannot be compiled into conditional effects if the plan size should be preserved. This implies that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan.