  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.
