Domains, probability measures and quantum theory
by
M. Mislove
Tulane Univ., USA

Domains originated in attempts to give semantic models for programming langauges, but about ten years ago, it became clear that domain theory had insights to offer in many other areas. In particular, the work of Abbas Edalat showed that domains could provide new approaches to such areas as integration. One of the accomplishments of domain theory that has received a lot of attention recently is its model of probabilistic computation. This requires giving a domain-theoretic presentation of the probability measures on a domain. In this talk, I'll describe how this is done, and point out how some classical results can be interpreted using domains. In addition, I'll decscribe some new results showing how domains arise in models of quantum computation - this last is recent work of Abramsky, Coecke and Martin at Oxford.

Date received: May 26, 2003