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VPSPACE and a Transfer Theorem over the Complex Field

  • Pascal Koiran
  • Sylvain Perifel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

Abstract

We extend the transfer theorem of [15] to the complex field. That is, we investigate the links between the class Open image in new window of families of polynomials and the Blum-Shub-Smale model of computation over Open image in new window . Roughly speaking, a family of polynomials is in Open image in new window if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) Open image in new window families can be evaluated efficiently then the class Open image in new window of decision problems that can be solved in parallel polynomial time over the complex field collapses to Open image in new window . As a result, one must first be able to show that there are Open image in new window families which are hard to evaluate in order to separate Open image in new window from Open image in new window , or even from Open image in new window .

Keywords

Polynomial Space Exponential Number Multivariate Polynomial Arithmetic Circuit Input Gate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Pascal Koiran
    • 1
  • Sylvain Perifel
    • 1
  1. 1.LIP*, École Normale Supérieure de Lyon 

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