Matches in SemOpenAlex for { <https://semopenalex.org/work/W2997389245> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W2997389245 startingPage "14" @default.
- W2997389245 abstract "In this paper we prove two results about AC^0[oplus] circuits.(1) We show that for d(N) = o(sqrt(log N/log log N)) and N {0,1}} such that - f_N has uniform AC^0 formulas of depth d and size at most s; - f_N does not have AC^0[oplus] formulas of depth d and size s^epsilon, where epsilon is a fixed absolute constant. This gives a quantitative improvement on the recent result of Limaye, Srinivasan, Sreenivasaiah, Tripathi, and Venkitesh, (STOC, 2019), which proved a similar Fixed-Depth Size-Hierarchy theorem but for d << log log N and s << exp(N^(1/2^Omega(d))). As in the previous result, we use the Coin Problem to prove our hierarchy theorem. Our main technical result is the construction of uniform size-optimal formulas for solving the coin problem with improved sample complexity (1/delta)^O(d) (down from (1/delta)^(2^O(d)) in the previous result).(2) In our second result, we show that randomness buys depth in the AC^0[oplus] setting. Formally, we show that for any fixed constant d >= 2, there is a family of Boolean functions that has polynomial-sized randomized uniform AC^0 circuits of depth d but no polynomial-sized (deterministic) AC^0[oplus] circuits of depth d.Previously Viola (Computational Complexity, 2014) showed that an increase in depth (by at least 2) is essential to avoid superpolynomial blow-up while derandomizing randomized AC^0 circuits. We show that an increase in depth (by at least 1) is essential even for AC^0[oplus]. As in Viola's result, the separating examples are promise variants of the Majority function on N inputs that accept inputs of weight at least N/2 + N/(log N)^(d-1) and reject inputs of weight at most N/2 - N/(log N)^(d-1)." @default.
- W2997389245 created "2020-01-10" @default.
- W2997389245 creator A5025305994 @default.
- W2997389245 creator A5077690880 @default.
- W2997389245 creator A5083072245 @default.
- W2997389245 date "2019-01-01" @default.
- W2997389245 modified "2023-09-28" @default.
- W2997389245 title "More on AC^0[oplus] and Variants of the Majority Function" @default.
- W2997389245 doi "https://doi.org/10.4230/lipics.fsttcs.2019.22" @default.
- W2997389245 hasPublicationYear "2019" @default.
- W2997389245 type Work @default.
- W2997389245 sameAs 2997389245 @default.
- W2997389245 citedByCount "1" @default.
- W2997389245 countsByYear W29973892452023 @default.
- W2997389245 crossrefType "proceedings-article" @default.
- W2997389245 hasAuthorship W2997389245A5025305994 @default.
- W2997389245 hasAuthorship W2997389245A5077690880 @default.
- W2997389245 hasAuthorship W2997389245A5083072245 @default.
- W2997389245 hasConcept C105795698 @default.
- W2997389245 hasConcept C114614502 @default.
- W2997389245 hasConcept C118615104 @default.
- W2997389245 hasConcept C121332964 @default.
- W2997389245 hasConcept C125112378 @default.
- W2997389245 hasConcept C134146338 @default.
- W2997389245 hasConcept C134306372 @default.
- W2997389245 hasConcept C14036430 @default.
- W2997389245 hasConcept C141796577 @default.
- W2997389245 hasConcept C162324750 @default.
- W2997389245 hasConcept C187455244 @default.
- W2997389245 hasConcept C195292467 @default.
- W2997389245 hasConcept C199360897 @default.
- W2997389245 hasConcept C2777027219 @default.
- W2997389245 hasConcept C2779557605 @default.
- W2997389245 hasConcept C31170391 @default.
- W2997389245 hasConcept C33923547 @default.
- W2997389245 hasConcept C34447519 @default.
- W2997389245 hasConcept C41008148 @default.
- W2997389245 hasConcept C62520636 @default.
- W2997389245 hasConcept C63553672 @default.
- W2997389245 hasConcept C77553402 @default.
- W2997389245 hasConcept C78458016 @default.
- W2997389245 hasConcept C86803240 @default.
- W2997389245 hasConcept C90119067 @default.
- W2997389245 hasConcept C90702460 @default.
- W2997389245 hasConceptScore W2997389245C105795698 @default.
- W2997389245 hasConceptScore W2997389245C114614502 @default.
- W2997389245 hasConceptScore W2997389245C118615104 @default.
- W2997389245 hasConceptScore W2997389245C121332964 @default.
- W2997389245 hasConceptScore W2997389245C125112378 @default.
- W2997389245 hasConceptScore W2997389245C134146338 @default.
- W2997389245 hasConceptScore W2997389245C134306372 @default.
- W2997389245 hasConceptScore W2997389245C14036430 @default.
- W2997389245 hasConceptScore W2997389245C141796577 @default.
- W2997389245 hasConceptScore W2997389245C162324750 @default.
- W2997389245 hasConceptScore W2997389245C187455244 @default.
- W2997389245 hasConceptScore W2997389245C195292467 @default.
- W2997389245 hasConceptScore W2997389245C199360897 @default.
- W2997389245 hasConceptScore W2997389245C2777027219 @default.
- W2997389245 hasConceptScore W2997389245C2779557605 @default.
- W2997389245 hasConceptScore W2997389245C31170391 @default.
- W2997389245 hasConceptScore W2997389245C33923547 @default.
- W2997389245 hasConceptScore W2997389245C34447519 @default.
- W2997389245 hasConceptScore W2997389245C41008148 @default.
- W2997389245 hasConceptScore W2997389245C62520636 @default.
- W2997389245 hasConceptScore W2997389245C63553672 @default.
- W2997389245 hasConceptScore W2997389245C77553402 @default.
- W2997389245 hasConceptScore W2997389245C78458016 @default.
- W2997389245 hasConceptScore W2997389245C86803240 @default.
- W2997389245 hasConceptScore W2997389245C90119067 @default.
- W2997389245 hasConceptScore W2997389245C90702460 @default.
- W2997389245 hasLocation W29973892451 @default.
- W2997389245 hasOpenAccess W2997389245 @default.
- W2997389245 hasPrimaryLocation W29973892451 @default.
- W2997389245 hasRelatedWork W1673132890 @default.
- W2997389245 hasRelatedWork W1919528438 @default.
- W2997389245 hasRelatedWork W194980229 @default.
- W2997389245 hasRelatedWork W2002068271 @default.
- W2997389245 hasRelatedWork W2094783265 @default.
- W2997389245 hasRelatedWork W2102477571 @default.
- W2997389245 hasRelatedWork W216666084 @default.
- W2997389245 hasRelatedWork W2167059462 @default.
- W2997389245 hasRelatedWork W2405004071 @default.
- W2997389245 hasRelatedWork W2407574188 @default.
- W2997389245 hasRelatedWork W2889078076 @default.
- W2997389245 hasRelatedWork W2894201019 @default.
- W2997389245 hasRelatedWork W2952360260 @default.
- W2997389245 hasRelatedWork W2982690488 @default.
- W2997389245 hasRelatedWork W3013938469 @default.
- W2997389245 hasRelatedWork W3037930063 @default.
- W2997389245 hasRelatedWork W3094152636 @default.
- W2997389245 hasRelatedWork W3177075103 @default.
- W2997389245 hasRelatedWork W3186058991 @default.
- W2997389245 hasRelatedWork W3199523595 @default.
- W2997389245 isParatext "false" @default.
- W2997389245 isRetracted "false" @default.
- W2997389245 magId "2997389245" @default.
- W2997389245 workType "article" @default.