IBS/KAIST Joint Discrete Math Seminar

Introduction to Boolean functions with Artificial Neural Network

Jon-Lark Kim (김종락)

Department of Mathematics, Sogang University, Seoul

Department of Mathematics, Sogang University, Seoul

2019/04/18 Thu 11:00AM-12:00PM (IBS, Room B232)

A Boolean function is a function from the set Q of binary vectors of length n (i.e., the binary n-dimensional hypercube) to F

_{2}={0,1}. It has several applications to complexity theory, digital circuits, coding theory, and cryptography.In this talk we give a connection between Boolean functions and Artificial Neural Network. We describe how to represent Boolean functions by Artificial Neural Network including linear and polynomial threshold units and sigmoid units. For example, even though a linear threshold function cannot realize XOR, a polynomial threshold function can do it. We also give currently open problems related to the number of (Boolean) linear threshold functions and polynomial threshold functions.