Developments in concurrent Kleene algebra

The laws are supported by a hierarchy of models, applicable and adaptable to a range of different purposes and to a range of different programming languages. The algebra is presented in three tiers. The bottom tier defines traces of program execution, represented as sets of events that have occurred in a particular run of a program; the middle tier defines a program as the set of traces of all its possible behaviours. The top tier introduces additional incomputable operators, which are useful for describing the desired or undesired properties of computer program behaviour. The final sections outline directions in which further research is needed.