Efficient and Private Property Testing via Indistinguishability
Cynthia Dwork, Pranay Tankala

TL;DR
This paper characterizes efficiently testable properties of Boolean functions based on symmetry and introduces a supersimulator concept, with implications for property testing, graph regularity, and indistinguishability.
Contribution
It provides a new equivalence for property testability based on structured symmetry and introduces the supersimulator concept for Boolean functions.
Findings
Characterization of testable properties via structured symmetry.
Introduction of the supersimulator concept for Boolean functions.
A new proof of the supersimulator lemma using graph regularity techniques.
Abstract
Given a small random sample of -bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from few samples and properties with structured symmetry, which depend only on the function's average values on an efficiently computable partition of the domain. Without the efficiency constraint, a similar characterization in terms of unstructured symmetry was obtained by Blais and Yoshida (2019). We also give a function testing analogue of the classic characterization of testable graph properties in terms of regular partitions, as well as a sublinear time and differentially private algorithm to compute concise summaries of such partitions of graphs. Finally, we tighten a recent characterization of the computational indistinguishability of product…
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