2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) 2022
DOI: 10.1109/focs52979.2021.00021
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Hardness vs Randomness, Revised: Uniform, Non-Black-Box, and Instance-Wise

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Cited by 10 publications
(23 citation statements)
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“…Let 𝑉 (𝑥, 𝑦) be a verifier for 𝐿, and assume that the witness length | 𝑦| is at most |𝑥|. 17 Then the randomized streaming algorithms 𝐴 considered in Theorem 1.3 can be further assumed to solve the search-version of 𝐿 with one-sided error in the following sense:…”
Section: Making Most Streaming Lower Bounds Constructive Implies Brea...mentioning
confidence: 99%
“…Let 𝑉 (𝑥, 𝑦) be a verifier for 𝐿, and assume that the witness length | 𝑦| is at most |𝑥|. 17 Then the randomized streaming algorithms 𝐴 considered in Theorem 1.3 can be further assumed to solve the search-version of 𝐿 with one-sided error in the following sense:…”
Section: Making Most Streaming Lower Bounds Constructive Implies Brea...mentioning
confidence: 99%
“…Recursive application of uniform hardness-randomness tradeoffs. One of our main ideas is to exploit very recent work on uniform hardness-randomness tradeoffs [CT21] which applies to generic computations, as long as they satisfy certain mild properties. These tradeoffs yield hitting sets rather than pseudorandom sets based on hardness -a hitting set H ⊆ {0, 1} M is a set that has non-empty intersection with every Q M ⊆ {0, 1} M that is dense (i.e., accepts at least a 1/poly(M ) fraction of strings) and is efficiently computable.…”
Section: Proof Ideasmentioning
confidence: 99%
“…Specifically, Chen and Tell [CT21] show that for any multi-output function f : {1 n } → {0, 1} n computed by uniform Boolean circuits of size T = T (n) and depth d = d(n), either there is a hitting set H ⊆ {0, 1} M computable in time poly(T ), or f (1 n ) can be computed with high probability in time (d + n) • poly(M ) (which could be much less than T ). Note that this tradeoff is applicable to any multi-output function f given bounds on its uniform circuit complexity.…”
Section: Proof Ideasmentioning
confidence: 99%
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