Behavioural Metrics via Functor Lifting - A Coalgebraic Approach

Explore a coalgebraic approach to behavioral metrics through functor lifting in this one-hour colloquium talk. Discover how behavioral distances of transition systems modeled via coalgebras for endofunctors extend traditional notions of behavioral equivalence into a quantitative framework where states are measured by their degree of similarity or dissimilarity. Learn about the category theoretic generalization of the Kantorovich/Wasserstein lifting from transportation theory applied to lifting functors to pseudo-metric spaces. Examine compositionality results that serve as essential components for adapting up-to-techniques to behavioral distances, including well-known coinductive methods for efficiently establishing lower bounds for behavioral metrics. Follow a detailed case study on probabilistic automata that demonstrates the practical application of these theoretical concepts. Gain insights into collaborative research spanning multiple institutions and contributors working on advanced topics in coalgebra, category theory, and quantitative behavioral analysis.