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VPSPACE and a Transfer Theorem over the Reals

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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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Dates and versions

ensl-00103018 , version 1 (03-10-2006)
ensl-00103018 , version 2 (31-01-2007)

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