Abstract
We extend the transfer theorem of [15] to the complex field. That is, we investigate the links between the class 
of families of polynomials and the Blum-Shub-Smale model of computation over 
. Roughly speaking, a family of polynomials is in 
if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) 
families can be evaluated efficiently then the class 
of decision problems that can be solved in parallel polynomial time over the complex field collapses to 
. As a result, one must first be able to show that there are 
families which are hard to evaluate in order to separate 
from 
, or even from 
.
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Koiran, P., Perifel, S. (2007). VPSPACE and a Transfer Theorem over the Complex Field. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_33
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DOI: https://doi.org/10.1007/978-3-540-74456-6_33
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