A Restricted Second-Order Logic for Non-deterministic Poly-Logarithmic Time

@article{Ferrarotti2020ARS,
  title={A Restricted Second-Order Logic for Non-deterministic Poly-Logarithmic Time},
  author={Flavio Ferrarotti and Sen{\'e}n Gonz{\'a}lez and Klaus-Dieter Schewe and Jos{\'e} Maria Turull Torres},
  journal={ArXiv},
  year={2020},
  volume={abs/1912.00010}
}
We introduce a restricted second-order logic $\mathrm{SO}^{\mathit{plog}}$ for finite structures where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. We demonstrate the relevance of this logic and complexity class by several problems in database theory. We then prove a Fagin's style theorem showing that the Boolean queries which can be expressed in the existential fragment of $\mathrm{SO}^{\mathit{plog}}$ corresponds exactly to… Expand
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