Abstract. The synthesis problem asks to construct a reactive finite-state system from an ω-regular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common reason for unrealizability is that assumptions on the environment of the system are incomplete. We study the problem of correcting an unrealizable specification ϕ by computing an environment assumption ψ such that the new specification ψ → ϕ is realizable. Our aim is to construct an assumption ψ that constrains only the environment and is as weak as possible. We present a two-step algorithm for computing assumptions. The algorithm operates on the game graph that is used to answer the realizability question. First, we compute a safety assumption that removes a minimal set of environment edges from the graph. Second, we compute a liveness assumption that puts fairness conditions on some of the remaining environment edges. We show that the problem of finding a minimal set of fair edges is computationally hard, and we use probabilistic games to compute a locally minimal fairness assumption.
In the area of assumption mining, Chatterjee et al. REF construct a minimal environment assumption based on removing edges from the game graph to ensure safety assumptions and then compute liveness assumptions to put additional fairness constraints on the remaining edges.
Environment Assumptions for Synthesis
ArXiv
ArXiv
Mathematics Computer Science