About: Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1}^Omega(n) -> {0,1}^n with minimum distance Omega(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: (1) If d=2 then w = Theta(n (log n/ log log n)^2). (2) If d=3 then w = Theta(n log log n). (3) If d=2k or d=2k+1 for some integer k > 1 then w = Theta(n lambda_k(n)), where lambda_1(n)=log n, lambda_{i+1}(n)=lambda_i^(n), and the -operation gives how many times one has to iterate the function lambda_i to reach a value at most 1 from the argument $n$. (4) If d=log^* n then w=O(n). Each bound is obtained for the first time in our paper. For depth d=2, our Omega(n (log n/log log n)^2) lower bound gives the largest known lower bound for computing any linear map, improving on the Omega(n log^{3/2} n) bound of Pudlak and Rodl (1994). We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1}^Omega(n) -> {0,1}^n with minimum distance Omega(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: (1) If d=2 then w = Theta(n (log n/ log log n)^2). (2) If d=3 then w = Theta(n log log n). (3) If d=2k or d=2k+1 for some integer k > 1 then w = Theta(n lambda_k(n)), where lambda_1(n)=log n, lambda_{i+1}(n)=lambda_i^(n), and the -operation gives how many times one has to iterate the function lambda_i to reach a value at most 1 from the argument $n$. (4) If d=log^* n then w=O(n). Each bound is obtained for the first time in our paper. For depth d=2, our Omega(n (log n/log log n)^2) lower bound gives the largest known lower bound for computing any linear map, improving on the Omega(n log^{3/2} n) bound of Pudlak and Rodl (1994). (en)
Title	Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates (en)
skos:prefLabel	Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates (en)
skos:notation	RIV/67985840:_____/12:00386309!RIV13-AV0-67985840
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(1M0545), P(GBP202/12/G061), P(IAA100190902)
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Koucký, Michal Pudlák, Pavel
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	174435
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/12:00386309
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	error correcting codes; bounded depth circuits; superconcentrators (en)
http://linked.open.../riv/klicoveSlovo	bounded depth circuits error correcting codes superconcentrators
http://linked.open...ontrolniKodProRIV	[5A5EED433FD9]
http://linked.open...v/mistoKonaniAkce	New York
http://linked.open...i/riv/mistoVydani	New York
http://linked.open...i/riv/nazevZdroje	Proceedings of the 44th symposium on Theory of Computing, STOC'2012
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI) Institute for Theoretical Computer Science Mathematical logic, complexity, and algorithms
http://linked.open...UplatneniVysledku	2012
http://linked.open...iv/tvurceVysledku	Koucký, Michal Pudlák, Pavel Gál, A. Hansen, K. A. Viola, E.
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2012-05-19 (xsd:date)
number of pages	26 (xsd:int)
http://bibframe.org/vocab/doi	10.1145/2213977.2214023
http://purl.org/ne...btex#hasPublisher	ACM
https://schema.org/isbn	978-1-4503-1245-5

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