LTL Reactive Synthesis with a Few Hints

Abstract

We study a variant of the problem of synthesizing Mealy machines that enforce LTL specifications against all possible behaviours of the environment, including hostile ones. In the variant studied here, the user provides the high level LTL specification $$\varphi $$ φ of the system to design, and a set E of examples of executions that the solution must produce. Our synthesis algorithm first generalizes the user-provided examples in E using tailored extensions of automata learning algorithms, while preserving realizability of $$\varphi $$ φ . Second, it turns the (usually) incomplete Mealy machine obtained by the learning phase into a complete Mealy machine realizing $$\varphi $$ φ . The examples are used to guide the synthesis procedure. We prove learnability guarantees of our algorithm and prove that our problem, while generalizing the classical LTL synthesis problem, matches its worst-case complexity. The additional cost of learning from E is even polynomial in the size of E and in the size of a symbolic representation of solutions that realize $$\varphi $$ φ , computed by the synthesis tool Acacia-Bonzai. We illustrate the practical interest of our approach on a set of examples.