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Property Testing with Online Adversaries

Authors Omri Ben-Eliezer , Esty Kelman , Uri Meir , Sofya Raskhodnikova

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Author Details

Omri Ben-Eliezer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Esty Kelman
  • Department of Computer Science and Faculty of Computing & Data Sciences, Boston University, MA, USA
  • CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA
Uri Meir
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Sofya Raskhodnikova
  • Department of Computer Science, Boston University, MA, USA

Funding

Research partly conducted while EK and UM were visiting the Simons Institute for the Theory of Computing.
  • Kelman, Esty: Supported by the Computer Science Department, Boston University. Supported in part by an Amazon Faculty Research Award to Arnab Bhattacharyya, in part by ERC grant 834735, and in part by NSF TRIPODS program (award DMS-2022448).

Acknowledgements

We thank Shachar Lovett for referring us to [Ben-Eliezer et al., 2012; Keevash and Sudakov, 2005], which led to the result in Section 4.

Cite AsGet BibTex

Omri Ben-Eliezer, Esty Kelman, Uri Meir, and Sofya Raskhodnikova. Property Testing with Online Adversaries. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.11

Abstract

The online manipulation-resilient testing model, proposed by Kalemaj, Raskhodnikova and Varma (ITCS 2022 and Theory of Computing 2023), studies property testing in situations where access to the input degrades continuously and adversarially. Specifically, after each query made by the tester is answered, the adversary can intervene and either erase or corrupt t data points. In this work, we investigate a more nuanced version of the online model in order to overcome old and new impossibility results for the original model. We start by presenting an optimal tester for linearity and a lower bound for low-degree testing of Boolean functions in the original model. We overcome the lower bound by allowing batch queries, where the tester gets a group of queries answered between manipulations of the data. Our batch size is small enough so that function values for a single batch on their own give no information about whether the function is of low degree. Finally, to overcome the impossibility results of Kalemaj et al. for sortedness and the Lipschitz property of sequences, we extend the model to include t < 1, i.e., adversaries that make less than one erasure per query. For sortedness, we characterize the rate of erasures for which online testing can be performed, exhibiting a sharp transition from optimal query complexity to impossibility of testability (with any number of queries). Our online tester works for a general class of local properties of sequences. One feature of our results is that we get new (and in some cases, simpler) optimal algorithms for several properties in the standard property testing model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Linearity testing
  • low-degree testing
  • Reed-Muller codes
  • testing properties of sequences
  • erasure-resilience
  • corruption-resilience

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