SPEAKER: Thomas T. Hildebrandt, ITU, the IT University of Copenhagen

DATE: Friday, 26 November 1999

PLACE and TIME: Room E3-209 at 14:15.

ABSTRACT: The lack of a universal computational model for concurrency has led to the proposal of a large number of different and often competing mathematical models in which to describe concurrent computational systems.

In this talk I will try to give an overview of my recently finished PhD-thesis. The thesis contributes to a categorical approach to semantics for concurrency aiming at a more coherent theory for concurrency, centered around the notion of bisimulation from open maps and presheaf models for concurrency.

My goal has been to extend earlier work on independence models for concurrency, and to take the first steps towards including two central topics in concurrency, viz. fairness and dataflow, that is, respectively an explicit partioning of computations into fair and unfair computations, and an explicit partioning of actions into input and output actions. These two topics have not been treated before in the categorical framework.

A result of the categorical approach will be that we can draw on the same general techniques to obtain and reason about models and semantics capturing different notions of observable behaviour and operational primitives.

First we will, not requiring any prior knowledge of category theory, describe the standard model for CCS-like process calculi (labelled trees or synchronisation trees) as a presheaf model, and Milner/Park's strong bisimulation as the canonical bisimulation from open maps. We then show how to give presheaf models for respectively fairness and dataflow. In both cases, models suggested by more ad hoc approaches reappear in the abstract setting, only on a much stronger fundament given by the general theory for presheaf models for concurrency developed through the last five years.