Dynamic Programming algorithm for Computing Temporal Logic Robustness

i ABSTRACT In this thesis we deal with the problem of temporal logic robustness estimation. We present a dynamic programming algorithm for the robust estimation problem of Metric Temporal Logic (MTL) formulas regarding a finite trace of time stated sequence. This algorithm not only tests if the MTL specification is satisfied by the given input which is a finite system trajectory, but also quantifies to what extend does the sequence satisfies or violates the MTL specification. The implementation of the algorithm is the DP-TALIRO toolbox for MATLAB. Currently it is used as the temporal logic robust computing engine of S-TALIRO which is a tool for MATLAB searching for trajectories of minimal robustness in Simulink/ Stateflow. DP-TALIRO is expected to have near linear running time and constant memory requirement depending on the structure of the MTL formula. DP-TALIRO toolbox also integrates new features not supported in its ancestor FW-TALIRO such as parameter replacement, most related iteration and most related predicate. A derivative of DP-TALIRO which is DP-T-TALIRO is also addressed in this thesis which applies dynamic programming algorithm for time robustness computation. We test the running time of DP-TALIRO and compare it with FW-TALIRO. Finally, we present an application where DP-TALIRO is used as the robustness computation core of S-TALIRO for a parameter estimation problem. ii ACKNOWLEDGEMENTS I want to thank Dr. Georgios Fainekos for this wonderful opportunity to work on this interesting research topic and more importantly work along with him. I benefit greatly from his guidance, rigorous attitude and forward-looking spirit. I appreciate the financial support from Dr. Georgios Fainekos and Arizona State University in the past two years. I would also like to thank Dr. Hessam Sarjoughian and Dr. Aviral.Shrivastava for the support and feedback they gave me as part of my thesis committee. helped and inspired me during past few years. Also, I want to thank all the professors and staffs of Arizona State University who altogether create a great learning and working environment and atmosphere for me. findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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