### Abstract

We provide a new algorithm to determine stuttering equivalence with time complexity O(m log n), where n is the number of states and m is the number of transitions of a Kripke structure. This algorithm can also be used to determine branching bisimulation in O(m(log |Act| + log n)) time, where Act is the set of actions in a labeled transition system.

Theoretically, our algorithm substantially improves upon existing algorithms, which all have time complexity of the form O(mn) at best. Moreover, it has better or equal space complexity. Practical results confirm these findings: they show that our algorithm can outperform existing algorithms by several orders of magnitude, especially when the Kripke structures are large.

The importance of our algorithm stretches far beyond stuttering equivalence and branching bisimulation. The known O(mn) algorithms were already far more efficient (both in space and time) than most other algorithms to determine behavioral equivalences (including weak bisimulation), and therefore they were often used as an essential preprocessing step. This new algorithm makes this use of stuttering equivalence and branching bisimulation even more attractive.

Theoretically, our algorithm substantially improves upon existing algorithms, which all have time complexity of the form O(mn) at best. Moreover, it has better or equal space complexity. Practical results confirm these findings: they show that our algorithm can outperform existing algorithms by several orders of magnitude, especially when the Kripke structures are large.

The importance of our algorithm stretches far beyond stuttering equivalence and branching bisimulation. The known O(mn) algorithms were already far more efficient (both in space and time) than most other algorithms to determine behavioral equivalences (including weak bisimulation), and therefore they were often used as an essential preprocessing step. This new algorithm makes this use of stuttering equivalence and branching bisimulation even more attractive.

Original language | English |
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Article number | 13 |

Journal | Acm Transactions on Computational Logic |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - 23 Jun 2017 |

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### Keywords

- branching bisimulation
- algorithm

### Cite this

Groote, J. F., Jansen, D. N., Keiren, J. J. A., & Wijs, A. J. (2017). An O(m log n) Algorithm for Computing Stuttering Equivalence and Branching Bisimulation.

*Acm Transactions on Computational Logic*,*18*(2), [13]. https://doi.org/10.1145/3060140