Interpolation-Based GR(1) Assumptions Refinement

Abstract

This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's interpolants. Our interpolation-based method identifies causes for unrealizability and computes assumptions that directly target unrealizable cores, without the need for user input. Thereby, we discuss how this property reduces the maximum number of steps needed to converge to realizability compared with other techniques. We describe properties of interpolants that yield helpful GR(1) assumptions and prove the soundness of the results. Finally, we demonstrate that our approach yields weaker assumptions than baseline techniques, and finds solutions in case studies that are unsolvable via existing techniques.