Sound and Complete Landmarks for And/Or Graphs

Landmarks for a planning problem are subgoals that are necessarily made true at some point in the execution of any plan. Since verifying that a fact is a landmark is PSPACE-complete, earlier approaches have focused on finding landmarks for the delete relaxation Π. Furthermore, some of these approaches have approximated this set of landmarks, although it has been shown that the complete set of causal delete-relaxation landmarks can be identified in polynomial time by a simple procedure over the relaxed planning graph. Here, we give a declarative characterisation of this set of landmarks and show that the procedure computes the landmarks described by our characterisation. Building on this, we observe that the procedure can be applied to any delete-relaxation problem and take advantage of a recent compilation of the m-relaxation of a problem into a problem with no delete effects to extract landmarks that take into account delete effects in the original problem. We demonstrate that this approach finds strictly more causal landmarks than previous approaches and discuss the relationship between increased computational effort and experimental performance, using these landmarks in a recently proposed admissible landmark-counting heuristic.