Query maintenance under batch changes with small-depth circuits
<|reference_start|>Query maintenance under batch changes with small-depth circuits: Which dynamic queries can be maintained efficiently? For constant-size changes, it is known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining many important queries, among them reachability, tree isomorphism, and the word problem for context-free languages. In other words, these queries are in the dynamic complexity class DynFO. We show that most of the existing results for constant-size changes can be recovered for batch changes of polylogarithmic size if one allows circuits of depth O(log log n) or, equivalently, first-order updates that are iterated O(log log n) times.<|reference_end|>
@article{datta2024query,
    title={Query maintenance under batch changes with small-depth circuits},
    author={Samir Datta, Asif Khan, Anish Mukherjee, Felix Tschirbs, Nils
  Vortmeier, Thomas Zeume},
    journal={arXiv preprint arXiv:2407.20031},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.20031},
    primaryClass={cs.LO cs.CC}
}