Strict Divergence for Probabilistic Timed Automata

Probabilistic timed automata are an extension of timed automata with discrete probability distributions. In previous work, a probabilistic notion of time divergence for probabilistic timed automata has been considered, which requires the divergence of time with probability 1. We show that this notion can lead to cases in which the probabilistic timed automaton satisfies a correctness requirement by making an infinite number of probabilistic transitions in a finite amount of time. To avoid such cases, we consider strict time divergence which concerns the divergence of time over all paths, rather than time divergence of paths with probability 1. We present new model-checking algorithms for probabilistic timed automata both for probabilistic and strict divergence. The algorithms have the same complexity as the previous model-checking algorithms for probabilistic timed automata.