Top-down lower bounds for depth-three circuits
Identifieur interne : 002928 ( Main/Exploration ); précédent : 002927; suivant : 002929Top-down lower bounds for depth-three circuits
Auteurs : J. H Stad [Suède] ; S. Jukna [Lituanie, Allemagne] ; P. Pudlák [République tchèque, Burundi]Source :
- computational complexity [ 1016-3328 ] ; 1995-06-01.
Abstract
Abstract: We present a top-down lower bound method for depth-three ⋎, ⋏, ¬-circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.
Url:
DOI: 10.1007/BF01268140
Affiliations:
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In particular, we prove that depth-three ⋎, ⋏, ¬-circuits that compute parity (or majority) require size at least $$2^{0.618...\sqrt n } (or 2^{0.849...\sqrt n } $$ , respectively). This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Burundi</li><li>Lituanie</li><li>République tchèque</li><li>Suède</li></country><region><li>Bohême centrale</li><li>Svealand</li></region><settlement><li>Prague</li><li>Stockholm</li></settlement></list><tree><country name="Suède"><region name="Svealand"><name sortKey="H Stad, J" sort="H Stad, J" uniqKey="H Stad J" first="J." last="H Stad">J. H Stad</name></region><name sortKey="H Stad, J" sort="H Stad, J" uniqKey="H Stad J" first="J." last="H Stad">J. H Stad</name></country><country name="Lituanie"><noRegion><name sortKey="Jukna, S" sort="Jukna, S" uniqKey="Jukna S" first="S." last="Jukna">S. 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