Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Finite Prediction of Recursive Real-Valued Functions

Speaker: Eiju Hirowatari
Author(s): Eiju Hirowatari, Kouichi Hirata and Tetsuhiro Miyahara
Slot: Tue, 11:30-11:50, Faraday D (col. 4)

Abstract

This paper concerns 
learning theory
of {\em recursive real-valued functions\/} 
that are one of the formulations for the computable real function.
Hirowatari et al. (2005) have introduced 
the finite prediction of recursive real-valued functions, 
which is based on a finite prediction machine 
that is a procedure to request finite examples 
of a recursive real-valued function f 
and a datum of a real number x, 
and to output a datum of a real number 
as the value of f(x). 
In this paper, 
we newly establish the interaction of 
the criterion RealFP for finite prediction of recursive real-valued functions 
and the criteria RealEx, RealCons, RealFin and RealNum! 
for inductive inference of recursive real-valued functions. 

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