Environment Assumptions for Synthesis

  • Authors:

  • Krishnendu Chatterjee;Thomas A. Henzinger;Barbara Jobstmann

  • Affiliations:

  • University of California, Santa Cruz;EPFL, Lausanne,;EPFL, Lausanne,

  • Venue:
  • CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
  • Year:
  • 2008

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Abstract

The synthesis problem asks to construct a reactive finite-state system from an 茂戮驴-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 φby computing an environment assumption 茂戮驴such that the new specification 茂戮驴茂戮驴φis realizable. Our aim is to construct an assumption 茂戮驴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.