•Theorem
PTIME=PSPACE ) IFP = PFP
•
•
•Proof. Supposes PTIME
= PSPACE. Consider a PFP formula f. It can be
expressed in two stages: first compute
a canonical structure, using IFP, then compute f0 (still a PFP) on
the canonical structure. The latter is PSPACE problem, hence in PTIME, and, since it is ordered, f0 can be expressed as IFP.