Selector Function¶
A selector function, denoted as \(f(x)\), serves as an alternative representation of an array \(A=[a_0, a_2, ..., a_n]\), where \(f(0) = a_0, f(1) = a_1, ..., f(n) = a_n\). This representation is achieved through Lagrange interpolation.
The primary purpose of a selector function is to “compress” multiple checks into a single operation. For instance, consider the need to verify an equation such as \(a_i + b_i = c_i\). In this scenario, three selectors \(A(x)\), \(B(x)\), and \(C(x)\) can be created, and the validation can be expressed as:
\[
\begin{aligned}
A(x) + B(x) = C(x)
\end{aligned}
\]
This approach streamlines the verification process by consolidating multiple checks into a more efficient single operation.