  In this paper, we study LTLf synthesis under environment specifications for
arbitrary reachability and safety properties. We consider both kinds of
properties for both agent tasks and environment specifications, providing a
complete landscape of synthesis algorithms. For each case, we devise a specific
algorithm (optimal wrt complexity of the problem) and prove its correctness.
The algorithms combine common building blocks in different ways. While some
cases are already studied in literature others are studied here for the first
time.
