Probabilistic Timed Automata with One Clock and Initialised Clock-Dependent Probabilities

Clock-dependent probabilistic timed automata extend classical timed automata with discrete probabilistic choice, where the probabilities are allowed to depend on the exact values of the clocks. Previous work has shown that the quantitative reachability problem for clock-dependent probabilistic timed automata with at least three clocks is undecidable. In this paper, we consider the subclass of clock-dependent probabilistic timed automata that have one clock, that have clock dependencies described by affine functions, and that satisfy an initialisation condition requiring that, at some point between taking edges with non-trivial clock dependencies, the clock must have an integer value. We present an approach for solving in polynomial time quantitative and qualitative reachability problems of such one-clock initialised clock-dependent probabilistic timed automata. Our results are obtained by a transformation to interval Markov decision processes.

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 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.