# Meaning of ⟨_⟩ in the context of verifiers

A verifier for a language A is an algorithm V, where $$A = \{w \mid V \text{ accepts \langle w,c \rangle for some string c}\}$$ ($c$ is called a certificate or proof)

What's the definition of $\langle , \rangle$ here?

• Not every question is about P vs NP. I think you should read up on the basics, starting with e.g. our reference questions. Anyway, the definition is probably given in the same source on an earlier page. What is your source, by the way? – Raphael Sep 18 '15 at 17:45

Any reasonable definition would do (I'll provide a formal definition later on). One simple definition, when $w,c$ are strings over some alphabet $\Sigma$ which doesn't contain the space character, is that $\langle w,c \rangle$ consists of $w$, a space, and $c$.
More generally, suppose that $\langle w,c \rangle_1$ and $\langle w,c \rangle_2$ are two definitions of the pairing function such that:
1. There exists a polytime function $f$ such that $f(\langle w,c \rangle_1) = \langle w,c \rangle_2$.
2. There exists a polytime function $g$ such that $g(\langle w,c \rangle_2) = \langle w,c \rangle_1$.
Then if we define NP using $\langle,\rangle_1$ and $\langle,\rangle_2$ we obtain the same class. A reasonable definition is one that satisfies (1) and (2) for the pairing function I described above.