  Temporal synthesis is the automated design of a system that interacts with an
environment, using the declarative specification of the system's behavior. A
popular language for providing such a specification is Linear Temporal Logic,
or LTL. LTL synthesis in the general case has remained, however, a hard problem
to solve in practice. Because of this, many works have focused on developing
synthesis procedures for specific fragments of LTL, with an easier synthesis
problem. In this work, we focus on Safety LTL, defined here to be the
Until-free fragment of LTL in Negation Normal Form~(NNF), and shown to express
a fragment of safe LTL formulas. The intrinsic motivation for this fragment is
the observation that in many cases it is not enough to say that something
"good" will eventually happen, we need to say by when it will happen. We show
here that Safety LTL synthesis is significantly simpler algorithmically than
LTL synthesis. We exploit this simplicity in two ways, first by describing an
explicit approach based on a reduction to Horn-SAT, which can be solved in
linear time in the size of the game graph, and then through an efficient
symbolic construction, allowing a BDD-based symbolic approach which
significantly outperforms extant LTL-synthesis tools.
