Colloquium Mathematics, Professor Joost-Pieter Katoen

Join us for coffee and tea at 15.30 p.m.

Title: Observing Stochastic Processes by Timed Automata

Abstract:

We consider the automated verification of a continuous-time Markov chain C.  For timed reachability objectives---can C reach a certain set of states within a deadline with a given likelihood---we show that this amounts to solving Volterra integral equation systems of the first type. Then, we consider the more general question of verifying CTMC C against a timed automaton A. The central problem is to compute the probability mass of runs in C that are accepted by A. We show that this can be solved by determining reachability probabilities in Davis' piecewise deterministic Markov processes.  In fact this amounts to solve Volterra integral equations of the second type.  For the special case of single clock timed automata, reachability probabilities in (our) PDMPs can be characterized by the least solution of a linear equation system, whose coefficients are ODE solutions.  We show that this can be done very efficiently by employing a graph decomposition of the PDMP.  This approach is amenable to bisimulation minimization and parallelization. Experiments with various examples from computer science as well as biology confirm that these optimizations lead to significant speed-ups.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: a.v.kiselev@rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/