Tight Bounds for Lifted HTN Plan Verification and Bounded Plan Existence

Plan verification is a canonical problem within any planning setting to ensure correctness. This problem is closely linked to the bounded plan existence problem. We analyze the complexity of these problems on lifted representations for Hierarchical Task Network (HTN) Planning. On top of the general analysis, we impose constraints on method orderings and the amount of tasks that methods decompose to. This pinpoints subclasses with lower complexity. Our results confirm the existence of more efficient algorithms when operating on the lifted, instead of grounded, representation.