Adler, I orcid.org/0000-0002-9667-9841, Köhler, N and Peng, P (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, Online. 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 |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 by SIAM. This is an author produced version of a conference paper 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: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Oct 2020 15:45 |
Last Modified: | 12 Dec 2024 15:38 |
Status: | Published |
Publisher: | ACM |
Identification Number: | 10.1137/1.9781611976465.96 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:166217 |