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.
- 2.Akshay, S., Bouyer, P., Krishna, S.N., Manasa, L., Trivedi, A.: Stochastic timed games revisited. In: Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). LIPIcs, vol. 58, pp. 8:1–8:14. Leibniz-Zentrum für Informatik (2016)Google Scholar
- 3.Akshay, S., Bouyer, P., Krishna, S.N., Manasa, L., Trivedi, A.: Stochastic timed games revisited. CoRR, abs/1607.05671 (2016)Google Scholar
- 7.Bouyer, P.: On the optimal reachability problem in weighted timed automata and games. In: Proceedings of the 7th Workshop on Non-Classical Models of Automata and Applications (NCMA 2015). email@example.com, vol. 318, pp. 11–36. Austrian Computer Society (2015)Google Scholar
- 9.D’Innocenzo, A., Abate, A., Katoen, J.: Robust PCTL model checking. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2012), pp. 275–286. ACM (2012)Google Scholar
- 10.Gregersen, H., Jensen, H.E.: Formal design of reliable real time systems. Master’s thesis, Department of Mathematics and Computer Science, Aalborg University (1995)Google Scholar
- 11.Hahn, E.M.: Model checking stochastic hybrid systems. Ph.D. thesis, Universität des Saarlandes (2013)Google Scholar
- 21.Segala, R.: Modeling and verification of randomized distributed real-time systems. Ph.D. thesis, Massachusetts Institute of Technology (1995)Google Scholar
- 22.Sproston, J.: Probabilistic timed automata with clock-dependent probabilities. CoRR (2017)Google Scholar