We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical relational systems but also, e.g. various forms of weighted systems and furthermore to flexibly combine existing system types. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time $\mathcal{O}(m\cdot \log n)$ where $n$ and $m$ are the numbers of nodes and edges, respectively. The generic complexity result and the possibility of combining system types yields a toolbox for efficient partition refinement algorithms. Instances of our generic algorithm match the run-time of the best known algorithms for unlabelled transition systems, Markov chains, deterministic automata (with fixed alphabets), Segala systems, and for color refinement.Comment: Extended journal version of the conference paper arXiv:1705.08362. Beside reorganization of the material, the introductory section 3 is entirely new and the other new section 7 contains new mathematical results

@article{abs-1806-05654,
  title = {Efficient and Modular Coalgebraic Partition Refinement},
  author = {Thorsten Wißmann and Ulrich Dorsch and Stefan Milius and Lutz Schröder},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 16, Issue 1},
  year = {2020},
  doi = {10.23638/lmcs-16(1:8)2020}
}