LTL_f synthesis with fairness and stability assumptions

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 LTL_f 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 LTL_f goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTL_f 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 LTL_f synthesis. In this work we show that in interesting cases we can avoid such a detour to LTL synthesis and keep the simplicity of LTL_f 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.