Typically-correct derandomization

Shaltiel, Ronen

doi:10.1145/1814370.1814389

Cited by 9 publications

(5 citation statements)

References 45 publications

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“…[GW02] pioneered the idea that randomized algorithms which are "typically correct" can be derandomized by harvesting randomness from the input itself. This idea has often been used for various kinds of derandomization tasks (see the surveys [Sha10,HW12] or the related work section in [Hoz17]).…”

Section: Harvesting Multiple Access Randomness From the Input: Hardne...mentioning

confidence: 99%

Logspace Reducibility From Secret Leakage Planted Clique

Mardia

2021

Preprint

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Section: Harvesting Multiple Access Randomness From the Input: Hardne...mentioning

confidence: 99%

Logspace Reducibility From Secret Leakage Planted Clique

Mardia

2021

Preprint

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“…• The proofs of [Zim07,Sha11] are based on a general framework, due to Goldreich and Wigderson [GW02], of "derandomization by extracting randomness from the input". (See [Sha10] for an excellent survey of this framework.) Both works use extractors within this framework to tame the correlations between the uniform random input (x ∼ {0, 1} n ) and the randomness employed by the query algorithm (r ∼ {0, 1} m ): Zimand uses exposure resilient extractors, and Shaltiel uses extractors for bit-fixing sources.…”

Section: Theorem 8 ([Zim07]mentioning

confidence: 99%

Constructive derandomization of query algorithms

Blanc¹,

Lange²,

Tan³

2019

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We give efficient deterministic algorithms for converting randomized query algorithms into deterministic ones. We first give an algorithm that takes as input a randomized q-query algorithm R with description length N and a parameter ε, runs in time poly(N ) • 2 O(q/ε) , and returns a deterministic O(q/ε)-query algorithm D that ε-approximates the acceptance probabilities of R. These parameters are near-optimal: runtime N + 2 Ω(q/ε) and query complexity Ω(q/ε) are necessary.Next, we give algorithms for instance-optimal and online versions of the problem:• Instance optimal: Construct a deterministic q ⋆ R -query algorithm D, where q ⋆ R is minimum query complexity of any deterministic algorithm that ε-approximates R.• Online: Deterministically approximate the acceptance probability of R for a specific input x in time poly(N, q, 1/ε), without constructing D in its entirety.Applying the techniques we develop for these extensions, we constructivize classic results that relate the deterministic, randomized, and quantum query complexities of boolean functions (Nisan, STOC 1989; Beals et al., FOCS 1998). This has direct implications for the Turing machine model of computation: sublinear-time algorithms for total decision problems can be efficiently derandomized and dequantized with a subexponential-time preprocessing step. Background: Non-constructive derandomization of query algorithmsWe begin by discussing two well-known results giving non-constructive derandomizations of query algorithms, where the first of the two efficiency criteria discussed above, the runtime of the derandomization procedure, is disregarded. These results establish the existence of a corresponding deterministic query algorithm, but their proofs do not yield efficient algorithms for constructing such a deterministic algorithm. Looking ahead, the main contribution of our work, described in detail in Section 2, is in obtaining constructive versions of these results.• In Section 1.2.1 we recall Yao's lemma [Yao77], specializing it to the context of query algorithms.For any randomized q-query algorithm R, (the "easy direction" of) Yao's lemma along with a standard empirical estimation analysis implies the existence of a deterministic O(q/ε)-query algorithm that ε-approximates R.

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“…Goldreich and Wigderson's idea of using the input as a source of randomness for a typicallycorrect derandomization [GW02] has been applied and developed by several researchers [AT04, vMS05, KS05, Zim08, Sha11, KvMS12, SW14, Alm19]; see related survey articles by Shaltiel [Sha10] and by Hemaspaandra and Williams [HW12]. Researchers have proven unconditional typically-correct derandomization results for several restricted models, including sublinear-time algorithms [Zim08,Sha11], communication protocols [Sha11,KvMS12], constant-depth circuits [Sha11,KvMS12], and streaming algorithms [Sha11].…”

Section: Related Workmentioning

confidence: 99%

Typically-Correct Derandomization for Small Time and Space

Hoza

2017

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Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n • poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n • poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique. * Supported by the NSF GRFP under Grant DGE-1610403 and by a Harrington Fellowship from UT Austin. 1 More generally, Klivans and van Melkebeek constructed a pseudorandom generator that fools size-T circuits on T input bits under this assumption. The generator has seed length O(log T ) and is computable in O(log T ) space.2 More generally, the Nisan-Zuckerman theorem applies as long as the original randomized algorithm for L uses only poly(S) random bits, regardless of how much time it takes.

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Typically-correct derandomization

Cited by 9 publications

References 45 publications

Logspace Reducibility From Secret Leakage Planted Clique

Logspace Reducibility From Secret Leakage Planted Clique

Constructive derandomization of query algorithms

Typically-Correct Derandomization for Small Time and Space

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