In this work, we present a formal language, CTML, to reason over probabilistic systems. CTML extends stochastic temporal logics in a way that it takes a real value as input and output a real value in the range of [ 0 , ∞ ) , as opposed to 0/1 values as input and output, and it can nest real values. This allows CTML to express a rich set of queries towards the unification of model checking and performance evaluation. In fact, CTML covers PCTL. It can express a nontrivial subset of PLTL formulas that cannot be expressed by PCTL. The significance of this result is that the overall complexity of CTML is linear, as opposed to exponential as it is with PLTL, in the size of the operators for a given formula, and polynomial in the size of a given model. Moreover, CTML can express real-valued performance queries such as: “if a system encounters a failure, what is the expected time to reach a recovery state?” that cannot be expressed by a probabilistic model checking logic, because they are “probabilistic” at most. Along with the specification language, we present a set of algorithms for the evaluation of the language and show proofs for their correctness. Additionally, we include an application example and show experimental results.

中文翻译：

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计算树测量语言 (CTML)

在这项工作中，我们提出了一种形式语言 CTML，用于对概率系统进行推理。CTML 扩展了随机时间逻辑，它以实数值作为输入，输出一个实数值，范围为 [ 0 , ∞ ) ，而不是 0/1 值作为输入和输出，它可以巢真正的价值观。这允许 CTML 表达一组丰富的查询，以统一模型检查和性能评估。事实上，CTML 涵盖了 PCTL。它可以表达不能用 PCTL 表达的 PLTL 公式的重要子集。这个结果的意义在于 CTML 的整体复杂性是线性的，与 PLTL 的指数相反，它在给定公式的运算符大小方面是线性的，在给定模型的大小方面是多项式的。此外，CTML 可以表达实值性能查询，例如：“如果系统遇到故障，达到恢复状态的预期时间是多少？” 这不能用概率模型检查逻辑来表达，因为它们最多是“概率的”。除了规范语言，我们提出了一套评估语言的算法，并展示了它们的正确性。此外，我们还提供了一个应用示例并展示了实验结果。