Let G = (V,Σ, S,R) be a context-free grammar in Chomsky Normal Form. We define a directed graph:
1. The set of vertices is V, the set of variables.
2. The set of directed edges is {(A,B) : A,B ∈ V and for some C ∈ V, either rule A → BC or rule A →
CB is in R}. We say that this graph is acyclic if it has no directed cycle, including no self-loops.
Show that if this graph is acyclic then grammar G generates a regular language