Arithmetic circuits: the chasm at depth four gets wider

In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2o(m) also admit arithmetic circuits of depth four and size 2o(m) . This theorem shows that for problems such as arithmetic circuit lower bounds or black-box derandomization of identity testing, the case of depth four circuits is in a certain sense the general case. In this paper we show that smaller depth four circuits can be obtained if we start from polynomial size arithmetic circuits. For instance, we show that if the permanent of n

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Pascal Koiran
• Keywords: Arithmetic Circuits, CORR 2010, Education, Polynomial, Polynomial Size