Diagonal Circuit Identity Testing and Lower Bounds

In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth-3 circuit C(x1, . . . , xn) (i.e. C is a sum of powers of linear functions) is zero. We also prove an exponential lower bound showing that such a circuit will compute determinant or permanent only if there are exponentially many linear functions. Our techniques generalize to the following new results:

• Type: Conference
• Year: 2007
• Where: DAGSTUHL
• Authors: Nitin Saxena
• Keywords: DAGSTUHL 2007, Deterministic Polynomial Time, Diagonal Depth-3 Circuit, Linear Functions, Software Engineering