Lecture 14 - Polynomial Identity Testing

In this lecture, we will see another foundational problem in algebraic complexity theory: the Polynomial Identity Testing (PIT) problem.

The PIT problem is the algebraic equivalent to the following “software testing” problem in computer science: given two programs, $P_1$ and $P_2$, determine whether they compute the same function. In other words, the PIT problem is to determine whether two algebraic circuits compute the same polynomial.

Polynomial Identity Testing

Given two algebraic circuits $C_1$ and $C_2$ computing polynomials $f$ and $g$, respectively, the Polynomial Identity Testing problem is to determine whether $f\equiv g$.