  We show that many infinite classes of permutations over finite fields can be
constructed via translators with a large choice of parameters. We first charac-
terize some functions having linear translators, based on which several
families of permutations are then derived. Extending the results of [10], we
give in several cases the compositional inverse of these permutations. The
connection with complete permutations is also utilized to provide further
infinite classes of permutations. Moreover, we propose new tools to study
permutations of the form x is mapped to x+(x^(p^m) - x+ lambda)^s and a few
infinite classes of permutations of this form are proposed.
