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- W1899254311 abstract "We extend the transfer theorem of [14] to the complex field. That is, we investigate the links between the class VPSPACE of families of polynomials and the Blum–Shub–Smale model of computation over C . Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently, then the class PAR C of decision problems that can be solved in parallel polynomial time over the complex field collapses to P C . As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate P C from NP C , or even from PAR C ." @default.
- W1899254311 created "2016-06-24" @default.
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- W1899254311 date "2009-11-01" @default.
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- W1899254311 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mstyle mathvariant=sans-serif><mml:mi>VPSPACE</mml:mi></mml:mstyle></mml:math> and a transfer theorem over the complex field" @default.
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- W1899254311 doi "https://doi.org/10.1016/j.tcs.2009.08.026" @default.
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