Stackelberg planning is a recently introduced single-turn two-player adversarial planning model, where two players are acting in a joint classical planning task, the objective of the first player being hampering the second player from achieving its goal. This places the Stackelberg planning problem somewhere between classical planning and general combinatorial two-player games. But, where exactly? All investigations of Stackelberg planning so far focused on practical aspects. We close this gap by conducting the first theoretical complexity analysis of Stackelberg planning. We show that in general Stackelberg planning is actually no harder than classical planning. Under a polynomial plan-length restriction, however, Stackelberg planning is a level higher up in the polynomial complexity hierarchy, suggesting that compilations into classical planning come with a worst-case exponential plan-length increase. In attempts to identify tractable fragments, we further study its complexity under various planning task restrictions, showing that Stackelberg planning remains intractable where classical planning is not. We finally inspect the complexity of meta-operator verification, a problem that has been recently connected to Stackelberg planning.

翻译：Stackelberg规划是一种近期引入的单轮双人对抗性规划模型，其中两个参与者在联合经典规划任务中行动，第一参与者的目标是阻碍第二参与者实现其目标。这使得Stackelberg规划问题介于经典规划与一般组合双人博弈之间。但具体处于何种位置？目前所有关于Stackelberg规划的研究均聚焦于实践层面。我们通过首次对Stackelberg规划进行理论复杂度分析来填补这一空白。研究表明，在一般情况下，Stackelberg规划的难度实际上并不高于经典规划。然而，在多形式规划长度限制下，Stackelberg规划在多项式复杂度层级中处于更高层级，这表明将其编译为经典规划会导致最坏情况下规划长度呈指数级增长。为识别可处理片段，我们进一步研究了各类规划任务限制下的复杂度，证明在经典规划可处理的情况下，Stackelberg规划仍保持难解性。最后，我们检验了近期与Stackelberg规划相关联的元算子验证问题的复杂度。