Pseudo-Boolean Proof Logging for Optimal Classical Planning

We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general framework for generating lower-bound certificates based on pseudo-Boolean constraints, which is agnostic to the planning algorithm used. As a case study, we show how to modify the $A^{*}$ algorithm to produce proofs of optimality with modest overhead, using pattern database heuristics and $h^\textit{max}$ as concrete examples. The same proof logging approach works for any heuristic whose inferences can be efficiently expressed as reasoning over pseudo-Boolean constraints.