We show that given a graph G we can CMSO-transduce its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who gave such transductions using order-invariant MSO, a strictly more expressive logic than CMSO. Our methods more generally yield C2MSO-transductions of the canonical decomposition of weakly-partitive set systems and weakly-bipartitive systems of bipartitions.

翻译：我们证明，给定图G，可以通过CMSO逻辑转换其模分解、分裂分解及双连接分解。这一结果改进了Courcelle在《计算机科学逻辑方法》（2006年）中的工作，其研究采用严格表达能力更强的序不变MSO逻辑实现此类转换。我们的方法更普遍地实现了弱可分集合系统与弱二分划分系统的规范分解的C2MSO转换。