A key technique for the verification of programs is counterexample-guided abstraction–refinement (CEGAR). Grumberg et al.
(LNCS, vol 3385, pp. 233–249. Springer, Berlin, 2005; Inf Comput 205(8):1130–1148, 2007) developed a CEGAR-based algorithm for the modal μ-calculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et al. is generalized
by ... [Show full abstract] presenting a new CEGAR-based algorithm for the μ-calculus. It is based on a more expressive abstract model and applies refinement only locally (at a single abstract state),
i.e., the lazy abstraction technique for safety properties is adapted to the μ-calculus. Furthermore, it separates refinement determination from the (3-valued based) model checking. Three different heuristics
for refinement determination are presented and illustrated.