Strategies synthesized using formal methods can be complex and often require infinite memory, which does not correspond to the expected behavior when trying to model Multi-Agent Systems (MAS). To capture such behaviors, natural strategies are a recently proposed framework striking a balance between the ability of agents to strategize with memory and the model-checking complexity, but until now has been restricted to fully deterministic settings. For the first time, we consider the probabilistic temporal logics PATL and PATL* under natural strategies (NatPATL and NatPATL*, resp.). As main result we show that, in stochastic MAS, NatPATL model-checking is NP-complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL* with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATL*.

翻译：使用形式化方法合成的策略通常较为复杂，且往往需要无限内存，这与建模多智能体系统(MAS)时的预期行为不符。为捕捉此类行为，自然策略作为一种新兴框架应运而生，它在智能体策略记忆能力与模型检验复杂度之间取得了平衡，但迄今为止仅适用于完全确定性环境。本文首次将概率时序逻辑PATL与PATL*扩展至自然策略框架（分别记为NatPATL与NatPATL*）。主要结果表明：在随机MAS中，当活跃联盟受限于确定性策略时，NatPATL模型检验的复杂度为NP完备；在相同限制下，NatPATL*的复杂度为2NEXPTIME。对于无限制情形，我们给出了NatPATL的EXPSPACE复杂度与NatPATL*的3EXPSPACE复杂度。