Reaction systems are a formal model for processes inspired by the functioning of the living cell. The underlying idea of this model is that the functioning of the living cell is determined by the interactions of biochemical reactions, and these interactions are based on the mechanisms of facilitation and inhibition. This project will investigate various notions of behavioural equivalence for reaction systems, aiming at the development of new efficient verification techniques for such notions.
Boolean nets are a family of Petri net models capable of describing a great range of computational systems, such as VLSI hardware systems or biologically motivated membrane systems or reaction systems. Recently there is a growing interest in the modelling of systems whose behaviour combines synchrony with asynchrony in a variety of complicated ways (in this case, synchrony is related to logical or physical closeness of system components, and asynchrony to the operation of distant or loosely connected subsystems).
You can find details of research projects that are currently active within ACiD (Algorithms and Complexity in Durham) at
We would welcome applications for PhD positions relating to any of these areas. For more project ideas see the School’s project pages.
Graphs, networks, and polygonal complexes are discrete geometric spaces appearing in countless theoretical contexts and applications (concrete practical examples are the World Wide Web, the Power Grid or social networks, but also polygon meshes in geometric modeling and 3D computer graphics). It is natural to introduce and to study local and global quantitative invariants for these discrete objects with the aim to measure their differences, to find strongly connected components, to construct and to work with good embeddings into Euclidean and non-Euclidean spaces, and to better understand their topology and other important properties.