Abstract.
We study the identity testing problem for depth 3 arithmetic circuits (\(\sum\prod\sum\) circuit). We give the first deterministic polynomial time identity test for \(\sum\prod\sum\) circuits with bounded top fanin. We also show that the rank of a minimal and simple \(\sum\prod\sum\) circuit with bounded top fanin, computing zero, can be unbounded. These results answer the open questions posed by Klivans–Spielman (STOC 2001) and Dvir–Shpilka (STOC 2005).
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Manuscript received 24 October 2006
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kayal, N., Saxena, N. Polynomial Identity Testing for Depth 3 Circuits. comput. complex. 16, 115–138 (2007). https://doi.org/10.1007/s00037-007-0226-9
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DOI: https://doi.org/10.1007/s00037-007-0226-9