What is it about?
In a sequence of articles, Moschovakis has proposed a mathematical modeling of the notion of algorithm—a set-theoretic “definition” of algorithms, much like the “definition” of real numbers as Dedekind cuts on the rationals or that of random variables as measurable functions on a probability space. Our main aim here is to investigate the important relation between an (implementable) algorithm and its implementations. A second aim is to fix some of the basic definitions in this theory, which have evolved since their introduction.
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Why is it important?
The relation between an (implementable) algorithm and its implementations is a significant aspect of our intuitions about algorithms.
Perspectives
The aim is to provide a traditional foundation for the theory of algorithms, a development of it within axiomatic set theory in the same way as analysis and probability theory are rigorously developed within set theory on the basis of the set theoretic modeling of their basic notions.
Vasilis Paschalis
National and Kapodistrian University of Athens
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This page is a summary of: Elementary Algorithms and Their Implementations, January 2008, Springer Science + Business Media,
DOI: 10.1007/978-0-387-68546-5_5.
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