Input-based Three-valued Abstraction Refinement

Abstract: Unlike Counterexample-Guided Abstraction Refinement (CEGAR), Three-Valued Abstraction Refinement (TVAR) is able to verify all properties of the mu-calculus. We present a novel algorithmic framework for TVAR that -- unlike the previous ones -- does not depend on modal transitions in the state space formalism. This entirely bypasses complications introduced to ensure monotonicity in previous frameworks and allows for simpler reasoning. The key idea, inspired by (Generalized) Symbolic Trajectory Evaluation and Delayed Nondeterminism, is to refine using abstract inputs rather than abstract states. We prove that the framework is sound, monotone, and complete, and evaluate a free and open-source implementation of an instantiation of the framework, demonstrating its ability to mitigate exponential explosion.