All reports by Author Sofya Raskhodnikova:

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TR20-174
| 18th November 2020
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Hadley Black, Iden Kalemaj, Sofya Raskhodnikova#### Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing

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TR19-163
| 16th November 2019
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Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Erik Waingarten#### Approximating the Distance to Monotonicity of Boolean Functions

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TR18-195
| 18th November 2018
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Sofya Raskhodnikova, Noga Ron-Zewi, Nithin Varma#### Erasures versus Errors in Local Decoding and Property Testing

Hadley Black, Iden Kalemaj, Sofya Raskhodnikova

We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions $f \colon \{0,1\}^d\to\mathbb{R}$. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function $f$ over an arbitrary partially ... more >>>

Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Erik Waingarten

We design a nonadaptive algorithm that, given a Boolean function $f\colon \{0,1\}^n \to \{0,1\}$ which is $\alpha$-far from monotone, makes poly$(n, 1/\alpha)$ queries and returns an estimate that, with high probability, is an $\widetilde{O}(\sqrt{n})$-approximation to the distance of $f$ to monotonicity. Furthermore, we show that for any constant $\kappa > ... more >>>

Sofya Raskhodnikova, Noga Ron-Zewi, Nithin Varma

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures.

Motivated by ... more >>>