Efficient Reactive Synthesis Using Mode Decomposition

Abstract: Developing critical components, such as mission controllers or embedded systems, is a challenging task. Reactive synthesis is a technique to automatically produce correct controllers. Given a high-level specification written in LTL, reactive synthesis consists of computing a system that satisfies the specification as long as the environment respects the assumptions. Unfortunately, LTL synthesis suffers from high computational complexity which precludes its use for many large cases. A promising approach to improve synthesis scalability consists of decomposing a safety specification into smaller specifications, that can be processed independently and composed into a solution for the original specification. Previous decomposition methods focus on identifying independent parts of the specification whose systems are combined via simultaneous execution. In this work, we propose a novel decomposition algorithm based on modes, which consists of decomposing a complex safety specification into smaller problems whose solution is then composed sequentially (instead of simultaneously). The input to our algorithm is the original specification and the description of the modes. We show how to generate sub-specifications automatically and we prove that if all sub-problems are realizable then the full specification is realizable. Moreover, we show how to construct a system for the original specification from sub-systems for the decomposed specifications. We finally illustrate the feasibility of our approach with multiple case studies using off-the-self synthesis tools to process the obtained sub-problems.