Generalized Implicit De nitions on Finite Structures

We propose a natural generalization of the concept of im plicit de nitions over nite structures allowing non determinism at an intermediate level of a deterministic de nition These generalized im plicit de nitions o er more expressive power than classical implicit de nitions Moreover their expressive power can be characterized over un ordered nite structures in terms of the complexity class NP co NP Finally we investigate a subclass of these where the non determinism is restricted to the choice of a unique relation with respect to an implicit linear order and prove that it captures UP co UP also over the class of all nite structures These results shed some light on the expressive power of non deterministic primitives