In this paper, we investigate the module-checking problem of pushdown multi-agent systems (PMS) against ATL and ATL* specifications. We establish that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same complexity as pushdown module-checking for CTL. On the other hand, we show that ATL* module-checking of PMS turns out to be 4EXPTIME-complete, hence exponentially harder than both CTL* pushdown module-checking and ATL* model-checking of PMS. Our result for ATL* provides a rare example of a natural decision problem that is elementary yet but with a complexity that is higher than triply exponential-time.

翻译：本文研究了下推多智能体系统（PMS）针对ATL和ATL*规范的模块检测问题。我们证明，对于ATL，PMS的模块检测是2EXPTIME完全的，这与CTL的下推模块检测具有相同的复杂度。另一方面，我们表明PMS的ATL*模块检测是4EXPTIME完全的，因此比CTL*下推模块检测和PMS的ATL*模型检测都指数级更难。我们关于ATL*的结果提供了一个罕见的自然判定问题的例子，该问题是初等的，但其复杂度高于三重指数时间。