Probabilistic Timed Automata with Clock-Dependent Probabilities
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 other hand, 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.
The inspiration for cdPTA arose from a discussion with Patricia Bouyer on the corner-point abstraction. Thanks also to Holger Hermanns, who expressed interest in a cdPTA-like formalism in a talk at Dagstuhl Seminar 14441.
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