Elsevier

Journal of Complexity

Volume 20, Issue 4, August 2004, Pages 523-528
Journal of Complexity

On invariance of degree for certain computations

https://doi.org/10.1016/j.jco.2003.11.007Get rights and content
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Abstract

We prove that a sequential or parallel machine in the Blum–Shub–Smale model, which recognizes the roots of an irreducible polynomial f(x,y) of degree n, in globally bounded time T, must actually compute a polynomial of degree n. This generalizes results of Cucker, and holds for polynomials and machines over an infinite ordered topological field and in certain cases over Z as well. It follows that in the Blum–Shub–Smale model with unit height, PNC for machines over Z.

Keywords

BSS machines
Continuous computational complexity

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Partially supported by PSC-CUNY Research Award 64476-00 33.