Adler, I., Köhler, N. and Peng, P. orcid.org/0000-0003-2700-5699 (2021) On testability of first-order properties in bounded-degree graphs. In: SODA '21: Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. SODA '21: ACM-SIAM Symposium on Discrete Algorithms, 10-13 Jan 2021, Virginia, Virtual Event. Association for Computing Machinery (ACM) , pp. 1578-1597. ISBN 9781611976465
Abstract
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix ∃*∀* is testable (i.e., testable with constant query complexity), while there exists an FO property that is expressible by a formula with quantifier prefix ∀*∃* that is not testable. In the dense graph model, a similar picture is long known (Alon, Fischer, Krivelevich, Szegedy, Combinatorica 2000), despite the very different nature of the two models. In particular, we obtain our lower bound by a first-order formula that defines a class of bounded-degree expanders, based on zig-zag products of graphs. We expect this to be of independent interest. We then prove testability of some first-order properties that speak about isomorphism types of neighbourhoods, including testability of 1-neighbourhood-freeness, and r-neighbourhood-freeness under a mild assumption on the degrees.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2020 Association for Computing Machinery. This is an author-produced version of a paper subsequently published in SODA '21: Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Oct 2020 09:33 |
Last Modified: | 19 Jan 2022 16:45 |
Published Version: | https://dl.acm.org/doi/abs/10.5555/3458064.3458160 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.5555/3458064.3458160 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:166524 |