On the Compilability and Expressive Power of Propositional Planning Formalisms (1106.0247v1)

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.

• The paper analyzes the expressive power and compilability of propositional planning formalisms using compilation schemes, showing how language features like conditional effects impact translation efficiency and plan size.
• It demonstrates that conditional effects significantly enhance expressive power, precluding translation into less expressive formalisms without exceeding linear plan size growth, although polynomial efficiency can be maintained with polynomial plan size increases.
• The analysis identifies equivalence classes of formalisms based on their expressiveness under plan-size-conserving compilation, offering a framework to evaluate the efficiency impact of adding new features to planning systems.

Analyzing the Compilability and Expressive Power of Propositional Planning Formalisms

The paper by Bernhard Nebel offers a comprehensive analysis of the expressive power and compilability of several propositional planning formalisms, extending from basic STRIPS to more complex systems integrating conditional effects, incomplete state specifications, and propositional formulae in preconditions. The work rigorously formalizes the concept of "expressive power" by introducing the notion of "compilation schemes," which are mappings between planning formalisms that aim to preserve the conciseness of planning domains and the resulting plan sizes.

One of the pivotal findings is the delineation of conditions under which various extensions to propositional planning formalisms impact their expressiveness and how these extended systems compare to one another. Particularly notable is the result that conditional effects in plan operators introduce significant expressive capacity that makes it computationally unreachable to translate these plans into systems without conditional effects without allowing significant growth in plan size, specifically beyond linear increase. The paper reveals that polynomial space efficiency can be maintained if polynomial increases in plan size are acceptable, a key insight for designing planning algorithms that aim for both expressiveness and efficiency.

Nebel's analysis identifies two equivalence classes within the examined formalism family with respect to expressiveness preserved under plan-size-conserving compilation schemes. The [ScIc] class includes those systems that can accommodate conditional effects and incomplete state specifications, while the [ScT] class embodies more rudimentary systems like basic STRIPS that do not have these capabilities. This distinction is critical, especially when considering the implications of adding language features to planning algorithms without heavily degrading efficiency.

From a complexity-theoretic viewpoint, the paper confirms that plan existence problems (e.g., PLANEX) for all scrutinized formalisms are PSPACE-complete, corroborating the fundamental limitations in computational tractability across this class of planning problems. Furthermore, through the construction and analysis of various hypothetical programming constructs and transformations, it delineates when particular enhancements to a planning formalism yield genuine increases in expressive power or are merely superficial.

The practical and theoretical insights afforded by this work provide firm guidance on how planning formalisms can be comparably measured for expressive ability, offering a robust framework for assessing the efficiency impact of adding new features. These insights hold promise for influencing the future development of AI planning systems by clarifying which extensions necessitate new algorithmic innovations versus those that allow existing frameworks to be adapted or compiled with minimal loss of planning efficacy.

This analysis leaves the door open for further explorations into even more expressive planning systems and invitations to future research into the field of AI planning that could capitalize on these findings. The complexity results challenge the AI community to ponder efficient, scalable methods for harnessing high expressiveness while combating the inherent intractability of the problem space. Subsequent efforts might involve the development of new compilation techniques, heuristic strategies or graph-based planning methodologies refined to handle conditional effects and richer languages with polynomial efficiency gains.