how to do this question about decidable language L3 G k IG i

how to do this question about decidable language

L3 (G, k) IG is a CFG that generates at least one string of length k)

Solution

L3 is a decidable language
We use the fact: that is If G is in CHOMSKY NORMAL FORM then we take any derivation of k has 2n 1
the following are the steps to solve the decidable language:
here we take n ,the n is the length of k.
Proof. The L3 for CFG is: On input <G, k>, where G is a CFG and k is a string:
1. Convert G to an equivalent one in Chomsky normal form.
2. List out of all derivations with 2n 1 steps, where n is the length of k.
3. On the off chance that any of these inferences create k, accept; otherwise, reject.