Compositional Safety LTL Synthesis

Reactive synthesis holds the promise of generating automatically a verifiably correct program from a high-level specification. A popular such specification language is Linear Temporal Logic (LTL). Unfortunately, synthesizing programs from general LTL formulas, which relies on first constructing a game arena and then solving the game, does not scale to large instances. The specifications from practical applications are usually large conjunctions of smaller LTL formulas, which inspires existing compositional synthesis approaches to take advantage of this structural information. The main challenge here is that they solve the game only after obtaining the game arena, the most computationally expensive part in the procedure. In this work, we propose a compositional synthesis technique to tackle this difficulty by synthesizing a program for each small conjunct separately and composing them one by one. While this approach does not work for general LTL formulas, we show here that it does work for Safety LTL formulas, a popular and important fragment of LTL. While we have to compose all the programs of small conjuncts in the worst case, we can prune the intermediate programs to make later compositions easier and immediately conclude unrealizable as soon as some part of the specification is found unrealizable. By comparing our compositional approach with a portfolio of all other approaches, we observed that our approach was able to solve a notable number of instances not solved by others. In particular, experiments on scalable conjunctive benchmarks showed that our approach scale well and significantly outperform current Safety LTL synthesis techniques. We conclude that our compositional approach is an important contribution to the algorithmic portfolio of Safety LTL synthesis.