Symmetries and Other Variations of "End-Recursive" HTN Problems: Mapping the Border Between Decidable and Undecidable Restrictions

In this paper, we investigate the complexity of determining if various restricted forms of hierarchical task network (HTN) planning have a plan. We perform a systematic analysis of new restrictions formed by applying symmetries and relaxations to two existing restrictions called regularity and tail-recursiveness. By doing so, we confirm that many variations on common restrictions do not affect the complexity of the plan existence problem. However, we also obtain the counter-intuitive result that combining some of these seemingly inert relaxations together renders the plan existence problem undecidable. Additionally, we unearth a critical difference in definitions between an early paper on HTN planning and modern formalisms that appears to have gone unnoticed.