On the Compilability and Expressive Power of Propositional Planning Formalisms

TL;DR

This paper formalizes the concept of expressive power in propositional planning formalisms through compilation schemes, analyzing how various extensions affect the ability to concisely represent planning domains and plans.

Contribution

It introduces a formal framework for comparing the expressiveness of planning formalisms via compilation schemes and provides key results on the limits of compiling certain features like conditional effects and propositional formulae.

Findings

Conditional effects cannot be compiled away with linear plan size growth

Conditional effects can be compiled with polynomial plan size growth

General propositional formulae cannot be compiled into conditional effects with linear plan size preservation

Abstract

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. 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 linearly. This implies that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan.