On well-separation of GR(1) specifications

Specifications for reactive synthesis, an automated procedure to obtain a correct-by-construction reactive system, consist of assumptions and guarantees. One way a controller may satisfy the specification is by preventing the environment from satisfying the assumptions, without satisfying the guarantees. Although valid this solution is usually undesired and specifications that allow it are called non-well-separated. In this work we investigate non-well-separation in the context of GR(1), an expressive fragment of LTL that enables efficient synthesis. We distinguish different cases of non-well-separation, and compute strategies showing how the environment can be forced to violate its assumptions. Moreover, we show how to find a core, a minimal set of assumptions that lead to non-well-separation, and further extend our work to support past-time LTL and patterns. We implemented our work and evaluated it on 79 specifications. The evaluation shows that non-well-separation is a common problem in specifications and that our tools can be efficiently applied to identify it and its causes.