Michael Bukatin
(Brandeis)

"Remarks on some methods for software continualization"

Domains with Scott topology represent the most popular continuous model of computations. They address an important concept of equivalence between programs and data by solving reflexive domain equations such as D=[D->D]. Elements of analysis on Scott domains, such as generalized metrics and continuous valuations, were developed, and, on the other hand, approximation models based on Scott domains were built for many conventional mathematical structures.However, while we can approximate conventional mathematical structures by Scott domains, we are still very far from developing equivalents of ordinary methods of engineering mathematics for Scott domains themselves, or for programs. Those who hope that further development of analysis on Scott domains would, for example, enable the use of standard optimization techniques on the spaces of programs are, so far, disappointed. Meanwhile, the approaches using more conventional mathematics for software continualization are emerging, such as embedding of imperative programs into analog neural nets by Neto, Siegelmann, and Costa, or continuous models for logic programs by Howard Blair et al. These approaches, however, do not yet offer a natural treatment of equivalence between programs and data.

The Colloquium is supported by generous contributions from the Bloomberg, Information Builders, Inc. and Netlogic, Inc.