Automatic Abstraction Refinement for Generalized Symbolic Trajectory Evaluation

In this paper, we present AutoGSTE, a comprehensive approach to automatic abstraction refinement for generalized symbolic trajectory evaluation (GSTE). This approach addresses imprecision of GSTE's quaternary abstraction caused by underconstrained input circuit nodes, quaternary state set unions, and existentially quantified-out symbolic variables. It follows the counterexample-guided abstraction refinement framework and features an algorithm that analyzes counterexamples (symbolic error traces) generated by GSTE to identify causes of imprecision and two complementary algorithms that automate model refinement and specification refinement according to the causes identified. AutoGSTE completely eliminates false negatives due to imprecision of quaternary abstraction. Application of AutoGSTE to benchmark circuits from small to large size has demonstrated that it can quickly converge to an abstraction upon which GSTE can either verify or falsify an assertion graph efficiently.