The resource-bounded alternating-time temporal logic RB±ATL combines strategic reasoning with reasoning about resources. Its model-checking problem is known to be 2exptime-complete (the same as its proper extension RB±ATL^⁎) and fragments have been identified to lower the complexity.

In this work, we consider the variant RB±ATL⁺ that allows for Boolean combinations of path formulae starting with single temporal operators, but restricted to a single resource, providing an interesting trade-off between temporal expressivity and resource analysis. We show that the model-checking problem for RB±ATL⁺ restricted to a single agent and a single resource is ${\mathrm{\Delta }}_2^{\mathrm{P}}$-complete, hence the same as for the standard branching-time temporal logic CTL⁺. In this case reasoning about resources comes at no extra computational cost. When a fixed finite set of linear-time temporal operators is considered, the model-checking problem drops to ptime, which includes the special case of RB±ATL restricted to a single agent and a single resource. Furthermore, we show that, with an arbitrary number of agents and a fixed number of resources, the model-checking problem for RB±ATL⁺ can be solved in exptime using a sophisticated Turing reduction to the parity game problem for alternating vector addition systems with states (AVASS).

资源有界交替时间逻辑RB ± ATL将战略推理与资源推理相结合。其模型检测问题被称为是2exptime -complete（同其合适的扩展RB ± ATL ^⁎）和片段已经确定，以降低复杂性。

在这项工作中，我们考虑了变体RB ± ATL ⁺，它允许从单个时间运算符开始的路径公式的布尔组合，但仅限于单个资源，在时间表达性和资源分析之间提供了一个有趣的权衡。我们表明RB ± ATL ⁺的模型检查问题仅限于单个代理和单个资源是${\mathrm{\Delta }}_2^{\mathrm{磷}}$-complete，因此与标准分支时间时序逻辑CTL ^{+ 相同}。在这种情况下，关于资源的推理不需要额外的计算成本。当考虑线性时间时间运算符的固定有限集时，模型检查问题下降到ptime，其中包括RB ± ATL仅限于单个代理和单个资源的特殊情况。此外，我们表明，使用任意数量的代理和固定数量的资源，RB ± ATL ⁺的模型检查问题可以在exptime 中解决 对具有状态的交替向量加法系统 (AVASS) 使用对奇偶博弈问题的复杂图灵约简。