Robust Sampling for MITL Specifications

Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification. Comments Postprint version. Published in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Volume 4763, Formal Modeling and Analysis of Timed Systems 5th International Conference, FORMATS 2007, Proceedings, October 2007, pages 147-162. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/330 Robust Sampling for MITL Specifications Georgios E. Fainekos and George J. Pappas School of Engineering and Applied Science, University of Pennsylvania {fainekos,pappasg}@seas.upenn.edu Abstract. Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification. Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification.