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Medientyp:
Elektronischer Konferenzbericht
Titel:
Lower Bounds for Multiplication via Network Coding
Beteiligte:
Afshani, Peyman
[VerfasserIn];
Freksen, Casper Benjamin
[VerfasserIn];
Kamma, Lior
[VerfasserIn];
Larsen, Kasper Green
[VerfasserIn]
Erschienen:
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik; LIPIcs - Leibniz International Proceedings in Informatics. 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), 2019
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, very recently proved by Harvey and van der Hoeven (2019), shows that two n-bit numbers can be multiplied via a boolean circuit of size O(n lg n). In this work, we prove that if a central conjecture in the area of network coding is true, then any constant degree boolean circuit for multiplication must have size Omega(n lg n), thus almost completely settling the complexity of multiplication circuits. We additionally revisit classic conjectures in circuit complexity, due to Valiant, and show that the network coding conjecture also implies one of Valiant's conjectures.