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Noncomputable Functions In The Blub-Shub-Smale Model, Wesley Calvert, Ken Kramer, Russell Miller
Noncomputable Functions In The Blub-Shub-Smale Model, Wesley Calvert, Ken Kramer, Russell Miller
Publications and Research
Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is insufficient to allow an oracle BSS-machine to decide membership in the set of algebraic numbers of degree d + 1. We add a number of further results on relative computability of these sets and their unions. Then we show that the halting problem for BSS-computation is not decidable below any countable oracle set, and give a more …