Special Case of Sat

From: Andreas Morgenstern (a_morgen_at_gmx.de)
Date: 10/15/04 

Date: Fri, 15 Oct 2004 11:03:43 +0200

Hi,
I hope anyone has an idea about the following:

It is well known that SAT for propostional formulas is NP-complete.
Now we restrict the boolean formulas to those formulas that are either
not satisfyable or satisfyable by exactly one assignment to the
variables in phi.

Example:
(x1 or x2) and (x1) does not lie in the above mentioned formula class,
because the satisfyability does not rely upon the assignment to x2.

When we now transfer SAT to this formula class, is the complexity higher
  or lower or is it equal ?

Thanks for all suggestions.

Greetings,

Andreas