Input-based Framework for Three-valued Abstraction Refinement

We present a novel algorithmic framework for Three-valued Abstraction Refinement, which extends Counterexample-guided Abstraction Refinement with the ability to verify all properties of mu-calculus including recovery (the ability of the system to always return to a certain state). The framework performs refinement on abstract system inputs rather than abstract states, avoiding problems of previous frameworks. We formalise input-based refinement by introducing the concept of generating automata, and prove that our framework is sound, monotone, and complete. We evaluate the usefulness of the framework on its implementation in our free and open-source formal verification tool.