# Decide if a string is a member of a language that represents $P$?

For some enumeration of the complexity class P (such as this as an example: How does an enumerator for machines for languages work?), for each string 𝑝 in the enumeration, does there exist some other string (certificate) 𝑐 that allows you to verify 𝑝 is a member of the enumeration in poly time? I believe that it might be possible in poly time because all we have to do is check if a string fits some certain format (format of the encoding)?

A decision problem $$P$$ is poly time verifiable iff there is an algorithm 𝑉 called verifier such that if $$P(w)=$$𝑌𝐸𝑆 then there is a string $$c$$ s.t. $$𝑉(w,c)=$$𝑌𝐸𝑆, if $$P(w)=𝑁𝑂$$ then for all strings $$c$$, $$𝑉(w,c)=$$𝑁𝑂 and V runs in $$O(w^{k})$$ for some constant $$k$$ for all inputs $$w$$.

This will allow you to check in poly time (not even requiring a verifier) whether a given string $$p$$ is a part of the enumeration