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August 22 – 27 , 2004, Dagstuhl Seminar 04351

Spatial Representation: Discrete vs. Continuous Computational Models

Organizers

Ralph Kopperman (City University of New York, US)
Michael B. Smyth (Imperial College London, GB)
Dieter Spreen (Universitšt Siegen, DE)
Julian Webster (Imperial College London, GB)

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Documents

List of Participants
Dagstuhl's Impact: Documents available

About the seminar

Topological notions and methods have been successfully applied in various areas of computer science. Programming language semantics and computing with exact real numbers are two important examples. Computerized geometrical constructions have many applications in engineering. The seminar will concentrate on an important approach which is basic to these applications, i.e. spatial representation.

Due to the digital nature of most applications, the structures used in computer science are different from the mathematical structures that are classically used in engineering and that are based on the continuum. Typical features of these digital structures are asymmetry and partiality. Whereas classical spaces contain only the ideal elements that are the result of a computation (approximation) process, spaces that also allow reasoning on such processes in a formal way must as well contain the partial (and finite) objects appearing during a computation. Only they can be observed in finite time.

The seminar was devoted to the study of several topological structures. The leading example of such is the domain (in Scott's sense), and it is closely related to locales. Here, the finitely observable properties of a process are the primary objects of study. The ideal entities, which are the first class citizens of classical mathematical structures, are obtained as derived objects. These have given rise to a constructive treatment of topological spaces, Formal Topology.

More about the seminar contents and talks in the Online Seminar Proceedings



Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


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