VPSPACE and a Transfer Theorem over the Reals

Abstract : We introduce a new class VPSPACE of families of polynomials. Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main theorem is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PAR of decision problems that can be solved in parallel polynomial time over the real numbers collapses to P. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate over the reals P from NP, or even from PAR.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00103018
Contributor : Sylvain Perifel <>
Submitted on : Wednesday, January 31, 2007 - 3:14:37 PM
Last modification on : Friday, January 25, 2019 - 3:34:10 PM
Long-term archiving on : Tuesday, September 21, 2010 - 12:30:46 PM

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Pascal Koiran, Sylvain Perifel. VPSPACE and a Transfer Theorem over the Reals. 2007. ⟨ensl-00103018v2⟩

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