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Topological aspects of numberings

✍ Scribed by Wolfram Menzel; Frank Stephan

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
330 KB
Volume
49
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We investigate connections between the syntactic and semantic distance of programs on an abstract, recursion theoretic level. For a certain rather restrictive notion of interdependency of the two kinds of distances, there remain only few and β€œunnatural” numberings allowing such close relationship. Weakening the requirements leads to the discovery of universal metrics such that for an arbitrary recursively enumerable family of functions a numbering compatible with such a metric can uniformly be constructed. We conclude our considerations with some implications on learning theory.

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