On the Complexity of Heuristic Synthesis for Satisficing Classical Planning: Potential Heuristics and Beyond

Abstract

Potential functions are a general class of heuristics for classical planning. For satisficing planning, previous work suggested the use of descending and dead-end avoiding (DDA) potential heuristics, which solve planning tasks by backtrack-free search. In this work we study the complexity of devising DDA potential heuristics for classical planning tasks. We show that verifying or synthesizing DDA potential heuristics is PSPACE-complete, but suitable modifications of the DDA properties reduce the complexity of these problems to the first and second level of the polynomial hierarchy. We also discuss the implications of our results for other forms of heuristic synthesis in classical planning.

Novelty vs. Potential Heuristics: A Comparison of Hardness Measures for Satisficing Planning

“…This implies that CC(Π) ≥ RM(Π). Helmert et al (Helmert et al 2022) studied multiple modifications of the DDA property. Each of them implies the WDDA property.…”

Higher-Dimensional Potential Heuristics: Lower Bound Criterion and Connection to Correlation Complexity

“…This corresponds to a direct encoding, too. Helmert (2006) showed an encoding of TMs into Promela tasks. However, this encoding does not fit our definition.…”

“…Finding the actual weights for such a potential heuristic is a hard problem and not the scope of this paper. It is PSPACE-complete in general and Σ p 2 -complete (that is the second level of the polynomial hierarchy) for heuristics with similar characteristics (Helmert et al 2022). (Seipp et al 2016) introduced 2 criteria based on operators to detect a lower bound of 2 for the correlation complexity.…”

On the Computational Complexity of Plan Verification, (Bounded) Plan-Optimality Verification, and Bounded Plan Existence

“…Automated planning is the task of finding a course of actions called a plan which achieves a certain goal. An immense effort has been devoted to studying the computational complexity of the plan existence problem in the context of both non-hierarchical (classical) planning (Erol, Nau, and Subrahmanian 1991;Bylander 1994;Helmert 2006; Bäckström and Jonsson 2011) and hierarchical planning (Erol, Hendler, and Nau 1996;Geier and Bercher 2011;Alford et al 2014;Alford, Bercher, and Aha 2015a,b;Bercher, Lin, and Alford 2022) which is to decide whether a planning problem has a solution. In contrast, the number of research endeavors on the complexity of deciding whether there exists a plan up to a certain length (the bounded plan existence problem) is relatively small which is a standard way to frame the problem of finding an optimal plan as a decision problem.…”