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FOCS
2007
IEEE

Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits

11 years 5 months ago
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty `Number on the Forehead' model. Our method is based on the notion of voting polynomial degree of functions and extends the Degree-Discrepancy Lemma in the recent work of Sherstov [24]. Using this we prove that depth three circuits consisting of a MAJORITY gate at the output, gates computing arbitrary symmetric function at the second layer and arbitrary gates of bounded fan-in at the base layer i.e. circuits of type MAJ SYMM ANYO(1) cannot simulate the circuit class AC0 in sub-exponential size. Further, even if the fan-in of the bottom ANY gates are increased to o(log log n), such circuits cannot simulate AC0 in quasi-polynomial size. This is in contrast to the classical result of Yao and Beigel-Tarui that shows that such circuits, having only MAJORITY gates, can simulate the class ACC0 in quasi-polynomial size when the bottom fan-in is increased ...
Arkadev Chattopadhyay
Added 16 Aug 2010
Updated 16 Aug 2010
Type Conference
Year 2007
Where FOCS
Authors Arkadev Chattopadhyay
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