**MSC:**- 28D05 Measure-preserving transformations
- 37A05 Measure-preserving transformations

are investigated in the setup of classical as well as of

relative ergodic theory. We present an explicit

construction of a finite one-sided generator for aperiodic

automorphisms with zero entropy. In the case of positive

entropy, we demonstrate the complexity of this task by

discussing an important example. Moreover, we provide a

generalisation of the Abramov-Rohlin-formula and prove

the existence of one-sided relative generators with finite

entropy.