What's decidable about linear loops?

Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Anton Varonka, Markus A. Whiteland, James Worrell 0001. What's decidable about linear loops?. Proceedings of the ACM on Programming Languages, 6(POPL):1-25, 2022. [doi]

@article{KarimovLOPVWW22,
  title = {What's decidable about linear loops?},
  author = {Toghrul Karimov and Engel Lefaucheux and Joël Ouaknine and David Purser and Anton Varonka and Markus A. Whiteland and James Worrell 0001},
  year = {2022},
  doi = {10.1145/3498727},
  url = {https://doi.org/10.1145/3498727},
  researchr = {https://researchr.org/publication/KarimovLOPVWW22},
  cites = {0},
  citedby = {0},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {6},
  number = {POPL},
  pages = {1-25},
}