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Arithmetic Circuits: A Chasm at Depth Four Manindra Agrawal

Summary: Arithmetic Circuits: A Chasm at Depth Four
Manindra Agrawal
Indian Institute of Technology, Kanpur
V Vinay
Geodesic Information Systems Ltd, Bangalore, and
Chennai Mathematical Institute, Chennai
August 12, 2008
We show that proving exponential lower bounds
on depth four arithmetic circuits imply exponen-
tial lower bounds for unrestricted depth arith-
metic circuits. In other words, for exponential
sized circuits additional depth beyond four does
not help.
We then show that a complete black-box de-
randomization of Identity Testing problem for
depth four circuits with multiplication gates of
small fanin implies a nearly complete derandom-
ization of general Identity Testing.
1 Introduction


Source: Agrawal, Manindra - Department of Computer Science and Engineering, Indian Institute of Technology Kanpur


Collections: Computer Technologies and Information Sciences