Can the Shor oracle be used to prove that a function is constant?

From: davidedc (davidedc_at_yahoo.com)
Date: 07/06/04 

Date: 6 Jul 2004 03:13:55 -0700

Given a function f:{0,1}^n --> {0,1}, would it be possible to use the
Shor Oracle to figure out if f is constant?

With this I mean: determine the period on the output qbit, obtained
applying a quantum implementation of f over the input qbits put in
superpositioned state. I guess that the period would be 1 iff the
function is constant?

If this was feasible, then P=NP because the SAT problem could be
addressed in polynomial time by performing a binary search on the
input space.

(Browsing through non-constant input spaces (properly setting selected
input qbits to 0 or 1), one could quickly converge to an input (if
any) which satisfies the given boolean function.)

Thanks,
Davide Della Casa