Circuit Complexity and Multiplicative Complexity of Boolean Functions

In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning different weights to XOR and AND gates.

• Type: Conference
• Year: 2010
• Where: CIE
• Authors: Arist Kojevnikov, Alexander S. Kulikov
• Keywords: Applied Computing, Boolean Circuit Complexity, CIE 2010, Circuit Complexity, Lower Bound