# The probabilistic powerdomain: Old problems and new results

(Birmingham)

Two approaches to the semantics of probabilistic processes arose around 1980; one by Kozen who employed Banach lattices (and tools from functional analysis) and another one by Saheb-Djahromi in the framework of Scott domains. My talk will follow the second line of investigation. Saheb-Djahromi's definition was considerably simplified by Jones and Plotkin in 1989, and a substantial amount of results were developed in the PhD dissertation of Jones. However, from a domain theoretic point of view, the theory contained some pitfalls and some fundamental questions remained open for some time (and some remain open to this day). More recently, it has become clear that a topological, rather than order-theoretic approach is more fruitful, and indeed, it has been relatively easy to establish the core properties one needs when working with the probabilistic powerspace: integration; extension of valuations to measures; closure in a suitable category of spaces. In this talk I wish to emphasize the underlying mathematical machinery which turned out to be quite elegant.

**Tuesday 2nd December 2003, 14:00**

Robert Recorde Room

Department of Computer Science