  In synthesis, assumptions are constraints on the environment that rule out
certain environment behaviors. A key observation here is that even if we
consider systems with LTLf goals on finite traces, environment assumptions need
to be expressed over infinite traces, since accomplishing the agent goals may
require an unbounded number of environment action. To solve synthesis with
respect to finite-trace LTLf goals under infinite-trace assumptions, we could
reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTLf and
in LTL have the same worst-case complexity (both 2EXPTIME-complete), the
algorithms available for LTL synthesis are much more difficult in practice than
those for LTLf synthesis. In this work we show that in interesting cases we can
avoid such a detour to LTL synthesis and keep the simplicity of LTLf synthesis.
Specifically, we develop a BDD-based fixpoint-based technique for handling
basic forms of fairness and of stability assumptions. We show, empirically,
that this technique performs much better than standard LTL synthesis.
