A Spectrum of Approximate Probabilistic Bisimulations
<|reference_start|>A Spectrum of Approximate Probabilistic Bisimulations: This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation that relates LMCs that can be made (exactly) probabilistically bisimilar by small perturbations of their transition probabilities. We explore how the notions interrelate and establish their connections to other well-known notions like $\varepsilon$-bisimulation.<|reference_end|>
@article{spork2024a,
    title={A Spectrum of Approximate Probabilistic Bisimulations},
    author={Timm Spork, Christel Baier, Joost-Pieter Katoen, Jakob Piribauer, Tim
  Quatmann},
    journal={arXiv preprint arXiv:2407.07584},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.07584},
    primaryClass={cs.LO}
}