Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version
<|reference_start|>Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version: In the context of spatial logics and spatial model checking for polyhedral models -- mathematical basis for visualisations in continuous space -- we propose a weakening of simplicial bisimilarity. We additionally propose a corresponding weak notion of $\pm$-bisimilarity on cell-poset models, a discrete representation of polyhedral models. We show that two points are weakly simplicial bisimilar iff their repesentations are weakly $\pm$-bisimilar. The advantage of this weaker notion is that it leads to a stronger reduction of models than its counterpart that was introduced in our previous work. This is important, since real-world polyhedral models, such as those found in domains exploiting mesh processing, typically consist of large numbers of cells. We also propose SLCS_eta, a weaker version of the Spatial Logic for Closure Spaces (SLCS) on polyhedral models, and we show that the proposed bisimilarities enjoy the Hennessy-Milner property: two points are weakly simplicial bisimilar iff they are logically equivalent for SLCS_eta. Similarly, two cells are weakly $\pm$-bisimilar iff they are logically equivalent in the poset-model interpretation of SLCS_eta. This work is performed in the context of the geometric spatial model checker PolyLogicA and the polyhedral semantics of SLCS.<|reference_end|>
@article{bezhanishvili2024weak,
    title={Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta --
  Extended Version},
    author={Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia, Mamuka Jibladze,
  Diego Latella, Mieke Massink, Erik P. de Vink},
    journal={arXiv preprint arXiv:2404.06131},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.06131},
    primaryClass={cs.LO}
}