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 PARR of decision problems that can be solved in parallel polynomial time over the real 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.

• Type: Conference
• Year: 2007
• Where: STACS
• Authors: Pascal Koiran, Sylvain Perifel
• Keywords: Parallel Polynomial Time, Polynomial, STACS 2007, Theoretical Computer Science, VPSPACE Families