RECURSIVELY-ENUMERABLE SUBSETS OF R-Q IN 2 COMPUTING MODELS BLUM-SHUB-SMALE MACHINE AND TURING MACHINE

In this paper we compare recursively enumerable subsets of R-q in two computing models over real numbers: the Blum-Shub-Smale machine and th e oracle Turing machine. We prove that any Turing RE open subset of R- q is a BSS RE Set, while a Turing RE closed set may not be a BSS RE se t. As an application we show that the Julia set of any computable hype rbolic polynomial is decidable in the Turing computing model. (C) 1998 -Elsevier Science B.V. All rights reserved.