Are there references of relations between logical functions and polynomials?

Question

I would appreciate any recommendations for references of relations between logical functions and polynomials.

Answer 1

Any function $\{0,1\}^n \to \{0,1\}$ can be represented as a polynomial in $\Bbb{F}_2[x_1,\ldots,x_n]$ and two polynomials $f,g$ give the same function iff $f-g = \sum_{j=1}^n (x_j^2-x_j) h_j$ for some polynomials $h_j$