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).
['Neeraj Kayal', 'Nitin Saxena']
Polynomial Identity Testing for Depth 3 Circuits