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This will be an OASIS duo, we will have two seminars: one 2-3, the other 3-4.

Bill Roscoe and Dana Scott ( Bill: OUCL, Dana: CMU and Visiting Fellow of Magdalen College )

Bill's title: Semantics based on linear observations

Bill's abstract: The semantics of CSP is traditionally based on linear observation models: a process is modelled by sets of observations that can be made of it linearly (i.e. not in branching time).  The best known are traces and failures-divergences. They automatically come with a theory of refinement and make standard operators distribute over nondeterministic choice.

I will explain what we know about the hierarchy of these models, and show how they correspond to particular ways of presenting operational and algebraic semantics, as well as contemplating the advantages and disadvantages of this style of semantics.

This talk will be a summary of Chapters 9-13 of my forthcoming book: "Understanding Concurrent Systems"

Dana's title: Semilattices, Domains, and Computability
Dana's abstract:  One popular notion of a (Scott-Ersov) domain is defined as a bounded complete algebraic cpo. Such an abstract a definition is not always so helpful for beginners.  The speaker found recently that there is an easy-to-construct domain of countable semilattices giving isomorphic copies of all countably based domains. This approach seems to have advantages over both the so-called "information systems" and more abstract lattice/ topological formulations, and it makes definitions of solutions to domain equations very elementary to justify.  The "domain of domains" also has a natural computable structure.

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