Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
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MS Teams (please email amgrad@uwaterloo.ca for the meeting link)
Zhibing Sun | Applied Mathematics, University of Waterloo
Verification of Stochastic Systems
We consider the verification of ω-regular properties of the discrete-time continuous-state stochastic systems. We adopt the abstraction-based method and use Interval-valued Markov chains(IMC) as our abstraction. We first introduce the verification of a reachability problem followed by the verification of $\omega$-regular properties of Markov chains. We give convergence analysis to the quantitative reachability problem. Then we give a detailed description of the behavior of interval-valued Markov chain.
We give a big picture of how to convert the verification of reachability problem from not solvable to solvable both theoretically and in practice. We first consider the optimization problems with memoryless adversaries, and then show that the history dependent ones would have no better performance. We show that the optimum solution exists, a local optimum is the global optimum, and the optimum solution of all the states can be achieved at the same time. We give algorithms for the qualitative maximum and minimum reachability problems. We give a detailed description and analysis of an algorithm for the quantitative maximum reachability problem. For the verification of ω-regular properties, we introduce the existing results and state the difficulties for the qualitative problem.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.