Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition probabilities can depend linearly on clock values. Clock-dependent probabilistic timed automata allow the modelling of a continuous relationship between time passage and the likelihood of system events. We show that the problem of deciding whether the maximum probability of reaching a certain location is above a threshold is undecidable for clock-dependent probabilistic timed automata. On the positive side, we show that the maximum and minimum probability of reaching a certain location in clock-dependent probabilistic timed automata can be approximated using a region-graph-based approach.

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具有时钟相关概率的概率定时自动机

概率定时自动机是经典定时自动机，在边缘上具有离散的概率分布。我们介绍了与时钟有关的概率定时自动机，这是概率定时自动机的一种变体，其中过渡概率可以线性地取决于时钟值。时钟相关的概率定时自动机允许对时间流逝与系统事件的可能性之间的连续关系进行建模。我们表明，对于依赖于时钟的概率定时自动机，无法确定到达某个位置的最大概率是否超过阈值的问题。从积极的一面，我们表明，可以使用基于区域图的方法来估计与时钟相关的定时自动机中到达某个位置的最大和最小概率。