Tobias Winkler

tobias.winkler at
Room 4231
Ahornstra├če 55
D-52074 Aachen

I am a PhD student in the Software Modeling and Verification Group headed by Professor J.-P. Katoen. Moreover, I am an associated doctoral researcher in the research training group UnRAVel.


My research is situated in the formal automatic analysis of probabilistic systems. In particular, my current research goals and interests include:

  • Parametric Markov Models
    In parametric Markov models such as Markov chains or MDPs, concrete probabilities may be replaced by real variables – the parameters. Parametric models are key to analyse situations were transition probabilities are unknown but not unrelated across the whole model; or to synthesise such probabilities in a way that a certain property holds. The main theoretical and practical difficulty are the global dependencies between the parameters. One of my research goals is to establish the theoretical complexity of pMDPs and to identify interesting tractable subclasses.
  • Stochastic Games
    In my Master’s thesis, I have been working on stochastic two-person games with multiple objectives. In the context of probabilistic model checking, stochastic games are commonly used as a powerful abstraction mechanism to obtain sound bounds on quantitative properties of otherwise huge Markovian models. I have investigated such games under lexicographic reachability objectives and conjunctions of thresholds on reachability properties.
  • Probabilistic Programming
    … is nowadays a common paradigm in machine learning. The increasing number of programmers and engineers writing such programs calls for rigorous automatic program analysis, just like for traditional software.

Thesis projects

If you are interested in writing a Bachelor/Master’s thesis in any of the areas mentioned above, don’t hesitate to contact me. You can also check our list of open topics.

Current thesis projects

I am currently supervising the following projects:


I’m currently involved in the following teaching activities: