Matches in SemOpenAlex for { <https://semopenalex.org/work/W223884710> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W223884710 startingPage "175" @default.
- W223884710 abstract "We show that the promise problem of distinguishing n-bit strings of relative Hamming weight $${1/2 + Omega(1/{rm lg}^{d-1} n)}$$ 1 / 2 + Ω ( 1 / lg d - 1 n ) from strings of weight $${1/2 - Omega(1/{rm lg}^{d - 1} n)}$$ 1 / 2 - Ω ( 1 / lg d - 1 n ) can be solved by explicit, randomized (unbounded fan-in) poly(n)-size depth-d circuits with error $${leq 1/3}$$ ≤ 1 / 3 , but cannot be solved by deterministic poly(n)-size depth-(d+1) circuits, for every $${d geq 2}$$ d ? 2 ; and the depth of both is tight. Our bounds match Ajtai's simulation of randomized depth-d circuits by deterministic depth-(d + 2) circuits (Ann. Pure Appl. Logic; '83) and provide an example where randomization buys resources.To rule out deterministic circuits, we combine Hastad's switching lemma with an earlier depth-3 lower bound by the author (Computational Complexity 2009).To exhibit randomized circuits, we combine recent analyses by Amano (ICALP '09) and Brody and Verbin (FOCS '10) with derandomization. To make these circuits explicit, we construct a new, simple pseudorandom generator that fools tests $${A_1 times A_2 times cdots times A_{{rm lg}{n}}}$$ A 1 × A 2 × ? × A lg n for $${A_i subseteq [n], |A_{i}| = n/2}$$ A i ⊆ [ n ] , | A i | = n / 2 with error 1/n and seed length O(lg n), improving on the seed length $${Omega({rm lg}, n, {rm lg}, {rm lg}, n)}$$ Ω ( lg n lg lg n ) of previous constructions." @default.
- W223884710 created "2016-06-24" @default.
- W223884710 creator A5072846764 @default.
- W223884710 date "2010-01-01" @default.
- W223884710 modified "2023-09-24" @default.
- W223884710 title "Randomness buys depth for approximate counting." @default.
- W223884710 hasPublicationYear "2010" @default.
- W223884710 type Work @default.
- W223884710 sameAs 223884710 @default.
- W223884710 citedByCount "4" @default.
- W223884710 crossrefType "journal-article" @default.
- W223884710 hasAuthorship W223884710A5072846764 @default.
- W223884710 hasConcept C105795698 @default.
- W223884710 hasConcept C11413529 @default.
- W223884710 hasConcept C114614502 @default.
- W223884710 hasConcept C118615104 @default.
- W223884710 hasConcept C121332964 @default.
- W223884710 hasConcept C125112378 @default.
- W223884710 hasConcept C134146338 @default.
- W223884710 hasConcept C134306372 @default.
- W223884710 hasConcept C140642157 @default.
- W223884710 hasConcept C141796577 @default.
- W223884710 hasConcept C163258240 @default.
- W223884710 hasConcept C187455244 @default.
- W223884710 hasConcept C18903297 @default.
- W223884710 hasConcept C19086982 @default.
- W223884710 hasConcept C2777759810 @default.
- W223884710 hasConcept C2779557605 @default.
- W223884710 hasConcept C2780992000 @default.
- W223884710 hasConcept C33923547 @default.
- W223884710 hasConcept C46757340 @default.
- W223884710 hasConcept C62520636 @default.
- W223884710 hasConcept C77553402 @default.
- W223884710 hasConcept C86803240 @default.
- W223884710 hasConcept C92913381 @default.
- W223884710 hasConceptScore W223884710C105795698 @default.
- W223884710 hasConceptScore W223884710C11413529 @default.
- W223884710 hasConceptScore W223884710C114614502 @default.
- W223884710 hasConceptScore W223884710C118615104 @default.
- W223884710 hasConceptScore W223884710C121332964 @default.
- W223884710 hasConceptScore W223884710C125112378 @default.
- W223884710 hasConceptScore W223884710C134146338 @default.
- W223884710 hasConceptScore W223884710C134306372 @default.
- W223884710 hasConceptScore W223884710C140642157 @default.
- W223884710 hasConceptScore W223884710C141796577 @default.
- W223884710 hasConceptScore W223884710C163258240 @default.
- W223884710 hasConceptScore W223884710C187455244 @default.
- W223884710 hasConceptScore W223884710C18903297 @default.
- W223884710 hasConceptScore W223884710C19086982 @default.
- W223884710 hasConceptScore W223884710C2777759810 @default.
- W223884710 hasConceptScore W223884710C2779557605 @default.
- W223884710 hasConceptScore W223884710C2780992000 @default.
- W223884710 hasConceptScore W223884710C33923547 @default.
- W223884710 hasConceptScore W223884710C46757340 @default.
- W223884710 hasConceptScore W223884710C62520636 @default.
- W223884710 hasConceptScore W223884710C77553402 @default.
- W223884710 hasConceptScore W223884710C86803240 @default.
- W223884710 hasConceptScore W223884710C92913381 @default.
- W223884710 hasLocation W2238847101 @default.
- W223884710 hasOpenAccess W223884710 @default.
- W223884710 hasPrimaryLocation W2238847101 @default.
- W223884710 hasRelatedWork W1551710240 @default.
- W223884710 hasRelatedWork W1988508518 @default.
- W223884710 hasRelatedWork W2347033974 @default.
- W223884710 hasRelatedWork W2401929940 @default.
- W223884710 hasRelatedWork W2567892222 @default.
- W223884710 hasRelatedWork W2788229924 @default.
- W223884710 hasRelatedWork W2937425078 @default.
- W223884710 hasRelatedWork W2949804052 @default.
- W223884710 hasRelatedWork W2950394272 @default.
- W223884710 hasRelatedWork W2951206720 @default.
- W223884710 hasRelatedWork W2951864299 @default.
- W223884710 hasRelatedWork W2952851418 @default.
- W223884710 hasRelatedWork W2963097553 @default.
- W223884710 hasRelatedWork W2963698105 @default.
- W223884710 hasRelatedWork W2977258328 @default.
- W223884710 hasRelatedWork W2999656158 @default.
- W223884710 hasRelatedWork W3082189405 @default.
- W223884710 hasRelatedWork W3102487001 @default.
- W223884710 hasRelatedWork W3179922198 @default.
- W223884710 hasRelatedWork W2182012087 @default.
- W223884710 hasVolume "17" @default.
- W223884710 isParatext "false" @default.
- W223884710 isRetracted "false" @default.
- W223884710 magId "223884710" @default.
- W223884710 workType "article" @default.