Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple decision diagram operation called Reach that also computes fixpoints. In contrast to saturation, it does not require a partitioning of the transition relation. We give sequential algorithms implementing the new operation for both binary and multi-valued decision diagrams, and moreover provide parallel counterparts. We implement these algorithms and experimentally compare their performance against saturation on 692 model checking benchmarks in different languages. The results show that the Reach operation often outperforms saturation, especially on transition relations with low locality. In a comparison between parallelized versions of Reach and saturation we find that Reach obtains comparable
speedups up to 16 cores, although falls behind saturation at 64 cores. Finally, in a comparison with the state-of-the-art model checking tool ITS-tools we find that Reach outperforms ITS-tools on 29% of models, suggesting that Reach can be useful as a complementary method in an ensemble tool.