Environment Assumptions for Synthesis

Chatterjee, Krishnendu; Henzinger, Thomas A.; Jobstmann, Barbara

Environment Assumptions for Synthesis

Authors

Chatterjee, Krishnendu

Henzinger, Thomas A.

Jobstmann, Barbara

Description

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 $ψ\toϕ$ 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.
15 pages