Has the same relation to E as UP does to P.

The class of languages L in UP such that the mapping from an input x to the unique witness for x is a permutation of L.

Contains P.

Defined in [HT03], where it was also shown that the closure of PermUP under polynomial-time one-to-one reductions is UP.

On the other hand, they show that if PermUP = UP then E = UE.