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Online Versus Offline Adversaries in Property Testing

Authors Esty Kelman , Ephraim Linder , Sofya Raskhodnikova

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LIPIcs.ITCS.2025.65.pdf
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Author Details

Esty Kelman
  • Boston University, MA, USA
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Ephraim Linder
  • Boston University, MA, USA
Sofya Raskhodnikova
  • Boston University, MA, USA

Funding

  • Kelman, Esty: Supported in part by the National Science Foundation under Grant No. 2022446 and in part by NSF TRIPODS program (award DMS-2022448).

Acknowledgements

The authors thank Uri Meir for fruitful discussions regarding the online model.

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Esty Kelman, Ephraim Linder, and Sofya Raskhodnikova. Online Versus Offline Adversaries in Property Testing. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.65

Abstract

We study property testing with incomplete or noisy inputs. The models we consider allow for adversarial manipulation of the input, but differ in whether the manipulation can be done only offline, i.e., before the execution of the algorithm, or online, i.e., as the algorithm runs. The manipulations by an adversary can come in the form of erasures or corruptions. We compare the query complexity and the randomness complexity of property testing in the offline and online models. Kalemaj, Raskhodnikova, and Varma (Theory Comput. `23) provide properties that can be tested with a small number of queries with offline erasures, but cannot be tested at all with online erasures. We demonstrate that the two models are incomparable in terms of query complexity: we construct properties that can be tested with a constant number of queries in the online corruption model, but require querying a significant fraction of the input in the offline erasure model. We also construct properties that exhibit a strong separation between the randomness complexity of testing in the presence of offline and online adversaries: testing these properties in the online model requires exponentially more random bits than in the offline model, even when they are tested with nearly the same number of queries in both models. Our randomness separation relies on a novel reduction from randomness-efficient testers in the adversarial online model to query-efficient testers in the standard model.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Property Testing
  • Online Adversary
  • Offline Adversary
  • Query Complexity
  • Randomness Complexity
  • Separations

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