LTLf Synthesis with Fairness and Stability Assumptions

Abstract: 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.