Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics

@article{Grebik2021ClassificationOL,
  title={Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics},
  author={Jan Greb'ik and V{\'a}clav Rozhoň},
  journal={ArXiv},
  year={2021},
  volume={abs/2103.14112}
}
We classify which local problems with inputs on oriented paths have so-called Borel solution and show that this class of problems remains the same if we instead require a measurable solution, a factor of iid solution, or a solution with the property of Baire. Together with the work from the field of distributed computing [Balliu et al. PODC 2019], the work from the field of descriptive combinatorics [Gao et al. arXiv:1803.03872, Bernshteyn arXiv:2004.04905] and the work from the field of random… 
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