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An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits

Authors Neeraj Kayal, Chandan Saha, Sébastien Tavenas

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Neeraj Kayal
Chandan Saha
Sébastien Tavenas

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Neeraj Kayal, Chandan Saha, and Sébastien Tavenas. An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.33

Abstract

We show an almost cubic lower bound on the size of any depth three arithmetic circuit computing an explicit multilinear polynomial in n variables over any field. This improves upon the previously known quadratic lower bound by Shpilka and Wigderson [CCC, 1999].

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Keywords
  • arithmetic circuits
  • depth-3 circuits
  • shifted partials

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