Ruben Turkenburg
(Co-)promotors: dr. J.C. (Jurriaan) Rot (RU) and prof. dr. J.H. (Herman) Geuvers (RU)
Radboud University
Date: 18 June 2026
Summary
State-transition systems are extensively used models in computer science. They consist of the states in which a system can exist, and transitions between these states indicating how the state can evolve. The computers which many of us use can be seen as having a state: the data they store, and transitions: the changes they make to these data to perform computations. In this thesis, we aim to better understand two main aspects of these models: how manipulations of systems affect their behaviour; and how to compare the behaviour of systems. For this, we use the theory of coalgebra to develop very generally applicable results.
The first part of this thesis gives a new approach for comparing the behaviour of systems (modelled as coalgebras) before and after transformations have been applied. Using this framework, we give new conditions under which transformations preserve and reflect the behaviour of systems. We apply these conditions to existing transformations (such as determinisation and ultrafilter extensions) as well as to obtain new conditions for important properties of modal logics: adequacy and expressivity.
The second part of the thesis further investigates how to compare system behaviour, specifically when systems exhibit different behaviours. We develop new notions of apartness between systems, and show how we can reason inductively about them. Our most important application is then to systems involving probabilistic transitions, for which we show how to prove a notion of behavioural apartness, and how to derive lower bounds on behavioural distances