(Lisboa (visiting Swansea))

The class of recursive functions over the reals, denoted by REC(R), wasintroduced by Cristopher Moore in his seminal paper written in 1995. Since

then many subsequent investigations brought new results: the class REC(R)

was put in relation with the class of functions generated by the General

Purpose Analog Computer of Claude Shannon; classical digital computation was

embedded in several ways into the new model of computation; restrictions of

REC(R) where seen to represent different classes of recursive functions, e.g.,

recursive, primitive recursive and elementary functions, and structures such

as the Ritchie and the Grzergorczyk hierarchies. The class of real recursive

functions was then stratified in a natural way, and REC(R) and the analytic

hierarchy were recently recognized as two faces of the same mathematical

concept.

In this new seminar, we bring a strong foundational support to the Real

Recursive Function Theory, rooted in Mathematical Analysis, in a way that

the reader can easily recognize both its intrinsic mathematical beauty and

its extreme simplicity. The new paradigm is now robust and smooth enough to

be taught. To achieve such a result some concepts had to change and some new

results were added.

(Joint work with Bruno Loff and Jerzy Mycka.)

Robert Recorde Room

Department of Computer Science