# Erasure-Resilient Property Testing

@article{Dixit2016ErasureResilientPT, title={Erasure-Resilient Property Testing}, author={Kashyap Dixit and Sofya Raskhodnikova and Abhradeep Thakurta and Nithin M. Varma}, journal={ArXiv}, year={2016}, volume={abs/1607.05786} }

Property testers form an important class of sublinear algorithms. In the standard property testing model, an algorithm accesses the input function f:D -> R via an oracle. With very few exceptions, all property testers studied in this model rely on the oracle to provide function values at all queried domain points. However, in many realistic situations, the oracle may be unable to reveal the function values at some domain points due to privacy concerns, or when some of the values get erased by… Expand

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#### 14 Citations

D S ] 2 0 Ju l 2 01 6 Erasure-Resilient Property Testing ∗

- 2016

Property testers form an important class of sublinear algorithms. In the standard property testing model, an algorithm accesses the input function f : D 7→ R via an oracle. With very few exceptions,… Expand

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We initiate the study of sublinear-time algorithms that access their input via an online adversarial oracle. After answering each query to the input object, such an oracle can erase or corrupt a… Expand

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It is shown that two fundamental properties of functions, linearity and quadraticity, can be tested for constant t with asymptotically the same complexity as in the standard property testing model and tight bounds in terms of t are proved. Expand

Erasure-Resilient Sublinear-Time Graph Algorithms

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- Electron. Colloquium Comput. Complex.
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The erasure-resilient algorithm (for the special case with no erasures) is an improvement over the previously known algorithm for connectedness in the standard property testing model and has optimal dependence on the proximity parameter $\varepsilon$. Expand

Parameterized Property Testing of Functions

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- Electron. Colloquium Comput. Complex.
- 2017

This work parameterizes the query complexity of property testers in terms of the size r of the image of the input function, and obtains testers for monotonicity and convexity of functions of the form f:[n]→ R with query complexity O (log r), with no dependence on n. Expand

C C ] 7 S ep 2 01 9 Hard properties with ( very ) short PCPPs and their applications

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We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed l, we construct a property P… Expand

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The results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form {0,1}^d and, more generally, [n]^d, in contrast to the situation for monotonicity testing where there is no adaptivity gap. Expand

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- Electron. Colloquium Comput. Complex.
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It is shown that the distance to monotonicity of real-valued functions that are $\alpha$-far from monotone can be approximated nonadaptively within a factor of $O(\sqrt{d\log d})$ with query complexity polynomial in $1/\alpha$ and the dimension $d$. Expand

Query complexity lower bounds for local list-decoding and hard-core predicates (even for small rate and huge lists)

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- Electron. Colloquium Comput. Complex.
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It is shown that black-box proofs cannot improve the Goldreich-Levin theorem and produce a hard-core predicate that is hard to predict with probability 12 + 1 `ω(1) when provided with a one-way function f : {0, 1} → { 0, 1}, such that circuits of size poly(`) cannot invert f with probability ρ = 1/2 √ `. Expand

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The two aspects of adaptivity and parameterization in sublinear-time algorithms for LIS estimation are investigated and it is implied that nonadaptive tolerant testing is strictly harder than non Adaptive erasure-resilient testing for the natural property of sortedness. Expand

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