Efficient approximate verification of B and Z models via symmetry markers

We present a new approximate verification technique for falsifying the invariants of B models. The technique employs symmetry of B models induced by the use of deferred sets. The basic idea is to efficiently compute markers for states, so that symmetric states are guaranteed to have the same marker (but not the other way around). The falsification algorithm then assumes that two states with the same marker can be considered symmetric. We describe how symmetry markers can be efficiently computed and empirically evaluate an implementation, showing both very good performance results and a high degree of precision (i.e., very few non-symmetric states receive the same marker). We also identify a class of B models for which the technique is precise and therefore provides an efficient and complete verification method. Finally, we show that the technique can be applied to Z models as well.