Is the following language decidable LG is a CFG such that LG

Is the following language decidable? L={|G is a CFG such that L(G)*=L(G)}

Solution

Answer:

The given language is undecidable.

We have given L (G)* = L(G)

G is CFG , but we can prove only two regular languages to be equal not for the CFG. Thus the L is undecidable.