Sciweavers

Share
JUCS
2008

The Computable Multi-Functions on Multi-represented Sets are Closed under Programming

11 years 5 months ago
The Computable Multi-Functions on Multi-represented Sets are Closed under Programming
: In the representation approach to computable analysis (TTE) [Grz55, i00], abstract data like rational numbers, real numbers, compact sets or continuous real functions are represented by finite or infinite sequences ( , ) of symbols, which serve as concrete names. A function on abstract data is called computable, if it can be realized by a computable function on names. It is the purpose of this article to justify and generalize methods which are already used informally in computable analysis for proving computability. As a simple formalization of informal programming we consider flowcharts with indirect addressing. Using the fact that every computable function on can be generated by a monotone and computable function on we prove that the computable functions on are closed under flowchart programming. We introduce generalized multi-representations, where names can be from general sets, and define realization of multi-functions by multi-functions. We prove that the function computed by ...
Klaus Weihrauch
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JUCS
Authors Klaus Weihrauch
Comments (0)
books