Journal of Complexity
Computational complexity over the p-adic numbers
Journal of Complexity
Complexity and real computation
Complexity and real computation
Lower Bounds in a Parallel Model without Bit Operations
SIAM Journal on Computing
P ≠ NC over the p-adic numbers
Journal of Complexity
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We prove that a sequential or parallel machine in the Blum-Shub-Smale model, which recognizes the roots of an irreducible polynomialf(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, P≠NC for machines over Z.