hm(P) = h1(Pm): Alternative Characterisations of the Generalisation From hmax To hm

The hm (m = 1 ...) family of admissible heuristics for STRIPS planning with additive costs generalise the hmax heuristic, which results when m = 1. We show that the step from h1 to hm can be made by changing the planning problem instead of the heuristic function. This furthers our understanding of the hm heuristic, and may inspire application of the same generalisation to admissible heuristics stronger than hmax. As an example, we show how it applies to the additive variant of hm obtained via cost splitting.