Top-down lower bounds for depth-three circuits
Identifieur interne : 000F69 ( Istex/Curation ); précédent : 000F68; suivant : 000F70Top-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.
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DOI: 10.1007/BF01268140
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H Stad</name><affiliation wicri:level="1"><mods:affiliation>Royal Institute of Technology, Stockholm, Sweden</mods:affiliation><country xml:lang="fr">Suède</country><wicri:regionArea>Royal Institute of Technology, Stockholm</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: johanh@nada.kth.se</mods:affiliation><country wicri:rule="url">Suède</country></affiliation></author><author><name sortKey="Jukna, S" sort="Jukna, S" uniqKey="Jukna S" first="S." last="Jukna">S. Jukna</name><affiliation wicri:level="1"><mods:affiliation>Institute of Mathematics, Vilnius, Lithuania</mods:affiliation><country xml:lang="fr">Lituanie</country><wicri:regionArea>Institute of Mathematics, Vilnius</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: jokna@ti.uni-trier.de</mods:affiliation><country wicri:rule="url">Allemagne</country></affiliation></author><author><name sortKey="Pudlak, P" sort="Pudlak, P" uniqKey="Pudlak P" first="P." last="Pudlák">P. 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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></record>Pour manipuler ce document sous Unix (Dilib)
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