Formal Methods for Stochastic Models: Algorithms and Applications

The formal analysis of stochastic models plays an important role in different disciplines of science, e.g., probability theory, evolutionary stochastic processes in biology.

In computer science, such models arise in formal verification of probabilistic systems, analysis of probabilistic programs, analysis of game-theoretic interactions with stochastic aspects, reasoning about randomized protocols, etc. At the heart of the analysis methods are algorithmic approaches that lead to automated tools.

Despite significant and impressive research achievements over the decades, many fundamental algorithmic problems related to formal analysis of stochastic models remain open.

Moreover, the emergence of new technologies and the need to build more complex systems, require faster and scalable algorithmic solutions. The overarching theme of the project is algorithmic approaches for formal methods to analyse stochastic models.

Our main research aims are: (1) Finite-state models: Develop faster explicit and implicit algorithms, and establish conditional lower bounds, for finite-state probabilistic systems. (2) Probabilistic programs: Develop efficient algorithmic approaches and practical techniques (e.g., compositional and abstraction techniques) for the analysis of probabilistic programs. (3) Stochastic and evolutionary games: Develop algorithmic approaches related to stochastic games and evolutionary games, which bring together the two different fields of game theory. (4) Application domains: Explore new application areas in diverse domains to demonstrate the effectiveness of the new algorithms developed.The projects success will significantly enrich formal methods for analysis of stochastic models that are crucial in the development of robust and correct systems.

Since stochastic models are foundational in several disciplines, the new algorithmic solutions are expected to lead to automated tools beneficial to other disciplines.