FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952360260> ?p ?o ?g. }

• W2952360260 abstract "The approximate degree of a Boolean function $f colon {-1, 1}^n rightarrow {-1, 1}$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. We introduce a generic method for increasing the approximate degree of a given function, while preserving its computability by constant-depth circuits. Specifically, we show how to transform any Boolean function $f$ with approximate degree $d$ into a function $F$ on $O(n cdot operatorname{polylog}(n))$ variables with approximate degree at least $D = Omega(n^{1/3} cdot d^{2/3})$. In particular, if $d= n^{1-Omega(1)}$, then $D$ is polynomially larger than $d$. Moreover, if $f$ is computed by a polynomial-size Boolean circuit of constant depth, then so is $F$. By recursively applying our transformation, for any constant $delta > 0$ we exhibit an AC$^0$ function of approximate degree $Omega(n^{1-delta})$. This improves over the best previous lower bound of $Omega(n^{2/3})$ due to Aaronson and Shi (J. ACM 2004), and nearly matches the trivial upper bound of $n$ that holds for any function. Our lower bounds also apply to (quasipolynomial-size) DNFs of polylogarithmic width. We describe several applications of these results. We give: * For any constant $delta > 0$, an $Omega(n^{1-delta})$ lower bound on the quantum communication complexity of a function in AC$^0$. * A Boolean function $f$ with approximate degree at least $C(f)^{2-o(1)}$, where $C(f)$ is the certificate complexity of $f$. This separation is optimal up to the $o(1)$ term in the exponent. * Improved secret sharing schemes with reconstruction procedures in AC$^0$." @default.
• W2952360260 created "2019-06-27" @default.
• W2952360260 creator A5066860235 @default.
• W2952360260 creator A5080601320 @default.
• W2952360260 date "2017-03-16" @default.
• W2952360260 modified "2023-09-27" @default.
• W2952360260 title "A Nearly Optimal Lower Bound on the Approximate Degree of AC$^0$" @default.
• W2952360260 cites W1502819076 @default.
• W2952360260 cites W1522263593 @default.
• W2952360260 cites W1569748117 @default.
• W2952360260 cites W1591959187 @default.
• W2952360260 cites W1614234223 @default.
• W2952360260 cites W1618756527 @default.
• W2952360260 cites W1671393514 @default.
• W2952360260 cites W1795584562 @default.
• W2952360260 cites W1964537764 @default.
• W2952360260 cites W1969865855 @default.
• W2952360260 cites W1971200845 @default.
• W2952360260 cites W1973728061 @default.
• W2952360260 cites W1981115804 @default.
• W2952360260 cites W2000070319 @default.
• W2952360260 cites W2009405883 @default.
• W2952360260 cites W2025070700 @default.
• W2952360260 cites W2025510995 @default.
• W2952360260 cites W2034038586 @default.
• W2952360260 cites W2035762900 @default.
• W2952360260 cites W2044859592 @default.
• W2952360260 cites W2058286540 @default.
• W2952360260 cites W2077740213 @default.
• W2952360260 cites W2086789740 @default.
• W2952360260 cites W2104038652 @default.
• W2952360260 cites W2106458073 @default.
• W2952360260 cites W2112553910 @default.
• W2952360260 cites W2114522915 @default.
• W2952360260 cites W2122780600 @default.
• W2952360260 cites W2144369373 @default.
• W2952360260 cites W2146956300 @default.
• W2952360260 cites W2158416399 @default.
• W2952360260 cites W2163361804 @default.
• W2952360260 cites W2173499948 @default.
• W2952360260 cites W2187292610 @default.
• W2952360260 cites W2216908642 @default.
• W2952360260 cites W2220094226 @default.
• W2952360260 cites W2328371232 @default.
• W2952360260 cites W2397763371 @default.
• W2952360260 cites W2405936819 @default.
• W2952360260 cites W2407602714 @default.
• W2952360260 cites W2547369620 @default.
• W2952360260 cites W2573933663 @default.
• W2952360260 cites W2576551362 @default.
• W2952360260 cites W2579489352 @default.
• W2952360260 cites W2610386774 @default.
• W2952360260 cites W2610739693 @default.
• W2952360260 cites W2611310478 @default.
• W2952360260 cites W2949361528 @default.
• W2952360260 cites W2949381943 @default.
• W2952360260 cites W2950662612 @default.
• W2952360260 cites W2963443482 @default.
• W2952360260 cites W2963914453 @default.
• W2952360260 cites W3104067947 @default.
• W2952360260 hasPublicationYear "2017" @default.
• W2952360260 type Work @default.
• W2952360260 sameAs 2952360260 @default.
• W2952360260 citedByCount "0" @default.
• W2952360260 crossrefType "posted-content" @default.
• W2952360260 hasAuthorship W2952360260A5066860235 @default.
• W2952360260 hasAuthorship W2952360260A5080601320 @default.
• W2952360260 hasConcept C114614502 @default.
• W2952360260 hasConcept C118615104 @default.
• W2952360260 hasConcept C121332964 @default.
• W2952360260 hasConcept C134306372 @default.
• W2952360260 hasConcept C14036430 @default.
• W2952360260 hasConcept C153658351 @default.
• W2952360260 hasConcept C164660894 @default.
• W2952360260 hasConcept C187455244 @default.
• W2952360260 hasConcept C199360897 @default.
• W2952360260 hasConcept C24890656 @default.
• W2952360260 hasConcept C2775997480 @default.
• W2952360260 hasConcept C2777027219 @default.
• W2952360260 hasConcept C2779557605 @default.
• W2952360260 hasConcept C33923547 @default.
• W2952360260 hasConcept C41008148 @default.
• W2952360260 hasConcept C62520636 @default.
• W2952360260 hasConcept C77553402 @default.
• W2952360260 hasConcept C78458016 @default.
• W2952360260 hasConcept C86803240 @default.
• W2952360260 hasConcept C90119067 @default.
• W2952360260 hasConceptScore W2952360260C114614502 @default.
• W2952360260 hasConceptScore W2952360260C118615104 @default.
• W2952360260 hasConceptScore W2952360260C121332964 @default.
• W2952360260 hasConceptScore W2952360260C134306372 @default.
• W2952360260 hasConceptScore W2952360260C14036430 @default.
• W2952360260 hasConceptScore W2952360260C153658351 @default.
• W2952360260 hasConceptScore W2952360260C164660894 @default.
• W2952360260 hasConceptScore W2952360260C187455244 @default.
• W2952360260 hasConceptScore W2952360260C199360897 @default.
• W2952360260 hasConceptScore W2952360260C24890656 @default.
• W2952360260 hasConceptScore W2952360260C2775997480 @default.
• W2952360260 hasConceptScore W2952360260C2777027219 @default.
• W2952360260 hasConceptScore W2952360260C2779557605 @default.

• next