# 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
2 Citations
Proper Hierarchies in Polylogarithmic Time and Absence of Complete Problems
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This paper shows that the descriptive complexity theory of polylogarithmic time is taken further showing that there are strict hierarchies inside each of the classes of the hierarchy. Expand
Completeness in Polylogarithmic Time and Space
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• ArXiv
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An alternative notion of completeness inspired by the concept of uniformity from circuit complexity is developed and proved and it is shown that complete problems can still play an important role in the study of the interrelationship between polylogarithmic and other classical complexity classes. Expand

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