VPSPACE and a Transfer Theorem over the Reals

Details VPSPACE and a Transfer Theorem over the Reals VPSPACE and a Transfer Theorem over the Reals

2006-10-03

arxiv.org/abs/cs/0610009v2

Computer Science

Computational Complexity

Full version of the paper (appendices of the first version are now included in the text)

Scientific paper

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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