We present the first study of robustness of systems that are both timed as well as reactive (I/O). We study the behavior of such timed I/O systems in the presence of uncertain inputs and formalize their robustness using the analytic notion of Lipschitz continuity: a timed I/O system is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions over timed words such as the timed version of the Manhattan distance and the Skorokhod distance. We consider two models of timed I/O systems — timed transducers and asynchronous sequential circuits. We show that K-robustness of timed transducers can be decided in polynomial space under certain conditions. For asynchronous sequential circuits, we reduce K-robustness w.r.t. timed Manhattan distances to K-robustness of discrete letter-to-letter transducers and show PSpace-completeness of the problem.
This research was supported in part by the European Research Council (ERC) under grant 267989 (QUAREM), by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE) and Z211-N23 (Wittgenstein Award), and by the National Science Centre (NCN), Poland under grant 2014/15/D/ST6/04543.
250 - 267
VMCAI: Verification, Model Checking and Abstract Interpretation
St. Petersburg, FL, USA
2016-01-17 – 2016-01-19
Henzinger TA, Otop J, Samanta R. Lipschitz robustness of timed I/O systems. In: Vol 9583. Springer; 2016:250-267. doi:10.1007/978-3-662-49122-5_12
Henzinger, T. A., Otop, J., & Samanta, R. (2016). Lipschitz robustness of timed I/O systems (Vol. 9583, pp. 250–267). Presented at the VMCAI: Verification, Model Checking and Abstract Interpretation, St. Petersburg, FL, USA: Springer. https://doi.org/10.1007/978-3-662-49122-5_12
Henzinger, Thomas A, Jan Otop, and Roopsha Samanta. “Lipschitz Robustness of Timed I/O Systems,” 9583:250–67. Springer, 2016. https://doi.org/10.1007/978-3-662-49122-5_12.
T. A. Henzinger, J. Otop, and R. Samanta, “Lipschitz robustness of timed I/O systems,” presented at the VMCAI: Verification, Model Checking and Abstract Interpretation, St. Petersburg, FL, USA, 2016, vol. 9583, pp. 250–267.
Henzinger TA, Otop J, Samanta R. 2016. Lipschitz robustness of timed I/O systems. VMCAI: Verification, Model Checking and Abstract Interpretation, LNCS, vol. 9583. 250–267.
Henzinger, Thomas A., et al. Lipschitz Robustness of Timed I/O Systems. Vol. 9583, Springer, 2016, pp. 250–67, doi:10.1007/978-3-662-49122-5_12.