If a grammar is of the following form (i.e. all its productions are), is its language regular?
- $B → a$ - where $B$ is a non-terminal in $N$ and a is a terminal in $Σ$
- $B → aC$ - where $B$ and $C$ are in $N$ and $a$ is in $Σ$
- $B → ε$ - where $B$ is in $N$ and $ε$ denotes the empty string, i.e. the string of length 0.
- $B → A$ - where $A$ and $B$ are non-terminals in $N$
(1. - 3. quoted from wikipedia)
I only added the 4th rule and I assume that the language is regular. However, I cannot find any reference that supports this intuition.