The synthesis problem asks to construct a reactive finite-state system from an omega-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 phi by computing an environment assumption psi such that the new specification psi -> phi is realizable. Our aim is to construct an assumption psi 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.
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CONCUR: Concurrency Theory
Chatterjee K, Henzinger TA, Jobstmann B. Environment assumptions for synthesis. In: Vol 5201. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2008:147-161. doi:10.1007/978-3-540-85361-9_14
Chatterjee, K., Henzinger, T. A., & Jobstmann, B. (2008). Environment assumptions for synthesis (Vol. 5201, pp. 147–161). Presented at the CONCUR: Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.1007/978-3-540-85361-9_14
Chatterjee, Krishnendu, Thomas A Henzinger, and Barbara Jobstmann. “Environment Assumptions for Synthesis,” 5201:147–61. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008. https://doi.org/10.1007/978-3-540-85361-9_14.
K. Chatterjee, T. A. Henzinger, and B. Jobstmann, “Environment assumptions for synthesis,” presented at the CONCUR: Concurrency Theory, 2008, vol. 5201, pp. 147–161.
Chatterjee K, Henzinger TA, Jobstmann B. 2008. Environment assumptions for synthesis. CONCUR: Concurrency Theory, LNCS, vol. 5201. 147–161.
Chatterjee, Krishnendu, et al. Environment Assumptions for Synthesis. Vol. 5201, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008, pp. 147–61, doi:10.1007/978-3-540-85361-9_14.