Stuttering equivalence is too slow!

Abstract: Groote and Wijs recently described an algorithm for deciding stuttering equivalence and branching bisimulation equivalence, acclaimed to run in $\mathcal{O}(m \log n)$ time. Unfortunately, the algorithm does not always meet the acclaimed running time. In this paper, we present two counterexamples where the algorithms uses $\Omega(md)$ time. A third example shows that the correction is not trivial. In order to analyse the problem we present pseudocode of the algorithm, and indicate the time that can be spent on each part of the algorithm in order to meet the desired bound. We also propose fixes to the algorithm such that it indeed runs in $\mathcal{O}(m \log n)$ time.