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 ...

• Type: Journal
• Year: 2008
• Where: JUCS
• Authors: Klaus Weihrauch
• Keywords: Computable, Computable Analysis, Computable Functions, JUCS 2008