Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00386309" target="_blank" >RIV/67985840:_____/12:00386309 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/2213977.2214023" target="_blank" >http://dx.doi.org/10.1145/2213977.2214023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2213977.2214023" target="_blank" >10.1145/2213977.2214023</a>
Alternative languages
Result language
angličtina
Original language name
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
Original language 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 thelargest known lower bound for computing any linear map, improving on the Omega(n log^{3/2} n) bound of Pudlak and Rodl (1994).
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 44th symposium on Theory of Computing, STOC'2012
ISBN
978-1-4503-1245-5
ISSN
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e-ISSN
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Number of pages
26
Pages from-to
479-494
Publisher name
ACM
Place of publication
New York
Event location
New York
Event date
May 19, 2012
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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