Efficient Evidence Generation for Modal $μ$-Calculus Model Checking (extended version)

Model checking is a technique to automatically assess whether a model of the behaviour of a system meets its requirements. Evidence explaining why the behaviour does (not) meet its requirements is essential for the user to understand the model checking result. Willemse and Wesselink showed that parameterised Boolean equation systems (PBESs), an intermediate format for $\mu$-calculus model checking, can be extended with information to generate such evidence. Solving the resulting PBES is much slower than solving one without additional information, and sometimes even impossible. In this paper we develop a two-step approach to solving a PBES with additional information: we first solve its core and subsequently use the information obtained in this step to solve the PBES with additional information. We prove the correctness of our approach and we have implemented it, demonstrating that it efficiently generates evidence using both explicit and symbolic solving techniques.