All reports by Author Justin Oh:

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TR24-165
| 21st October 2024
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Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman#### Online Condensing of Unpredictable Sources via Random Walks

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TR23-056
| 26th April 2023
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Geoffrey Mon, Dana Moshkovitz, Justin Oh#### Approximate Locally Decodable Codes with Constant Query Complexity and Nearly Optimal Rate

Revisions: 2

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TR22-103
| 15th July 2022
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Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman#### Almost Chor--Goldreich Sources and Adversarial Random Walks

Revisions: 2

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TR19-099
| 29th July 2019
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Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman#### Nearly Optimal Pseudorandomness From Hardness

Revisions: 3

Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman

A natural model of a source of randomness consists of a long stream of symbols $X = X_1\circ\ldots\circ X_t$, with some guarantee on the entropy of $X_i$ conditioned on the outcome of the prefix $x_1,\dots,x_{i-1}$. We study unpredictable sources, a generalization of the almost Chor--Goldreich (CG) sources considered in [DMOZ23]. ... more >>>

Geoffrey Mon, Dana Moshkovitz, Justin Oh

We present simple constructions of good approximate locally decodable codes (ALDCs) in the presence of a $\delta$-fraction of errors for $\delta<1/2$. In a standard locally decodable code $C \colon \Sigma_1^k \to \Sigma_2^n$, there is a decoder $M$ that on input $i \in [k]$ correctly outputs the $i$-th symbol of a ... more >>>

Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman

A Chor--Goldreich (CG) source [CG88] is a sequence of random variables $X = X_1 \circ \ldots \circ X_t$, each $X_i \sim \{0,1 \{^d$, such that each $X_i$ has $\delta d$ min-entropy for some constant $\delta > 0$, even conditioned on any fixing of $X_1 \circ \ldots \circ X_{i-1}$. We typically ... more >>>

Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman

Existing proofs that deduce $\mathbf{BPP}=\mathbf{P}$ from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against nondeterministic circuits, we convert any randomized algorithm over inputs of length $n$ running in ... more >>>