VPSPACE and a transfer theorem over the reals

Authors:
Pascal Koiran;Sylvain Perifel
Affiliations:
LIP, École Normale Supérieure de Lyon;LIP, École Normale Supérieure de Lyon
Venue:
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Year:
2007

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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 PARR of decision problems that can be solved in parallel polynomial time over thereal numbers collapses to PR. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate PR from NPR, or even from PARR.