Amplifying Lower Bounds by Means of Self-Reducibility
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F08%3A00318523" target="_blank" >RIV/67985840:_____/08:00318523 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Amplifying Lower Bounds by Means of Self-Reducibility
Original language description
We observe that many important computational problems in NC^1 share a simple self-reducibility property. We then show that, for any problem A having this self-reducibility property. A has polynomial size TC^0 circuits if and only if it has TC^0 circuitsof size $n^{1+/epsilon}$for every/epsilon >0(counting the number of wires in a circuit as the size of the circuit). As an example of what this observation yields, consider the Boolean Formula Evaluation problem (BFE), which is complete for NC^1. It follows from a lower bound of Impagliazzo, Paturi, and Saks, that BFE requires depth d TC^0 circuits of size $n^{1+/epsilon_d}$. If one were able to improve this lower bound to show that there is some constant /epsilon>0 such that every TC^0 circuit family recognizing BFE has size $n^{1+/epsilon}$, then it would follow that TC^0/not=NC^1.
Czech name
Zesilování dolních odhadů pomocí dolů samopřevoditelnosti
Czech description
Článek se zabývá dolními odhady ve výpočetní složitosti.
Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GP201%2F07%2FP276" target="_blank" >GP201/07/P276: Computational and communication complexity of Boolean functions, and derandomization</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2008
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 IEEE Conference on Computational Complexity 2008
ISBN
978-0-7695-3169-4
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
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Publisher name
IEEE Computer Society Press
Place of publication
Maryland
Event location
College Park
Event date
Jun 23, 2008
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000257941800004