I stumble across this problem:
The solution given was simple:
Earlier I came across problems specified in this post, which involves applying Arden's theorem to left linear and right linear equations to find regular expressions. So I thought whether I can come up with left linear grammar for this. I tried and come up with this grammar:
$S\rightarrow \epsilon | Sa$
I was doubting if it is correct. So I tried operating both grammars on string "ab".
For right linear grammar, instantaneous description will be:
$S\Rightarrow aS \Rightarrow abA\Rightarrow ab$
For left linear grammar, I felt it should be:
$A\Rightarrow Sb\Rightarrow Sab\Rightarrow ab$
As you can see, above derivation in left linear grammar doesnt start with $S$ but ends with $S$ (i.e. uses production $S\rightarrow \epsilon$ in the end). So is it correct to think as valid derivation and legit left linear grammar? Also can we interpret it as something like bottom up derivation? I know I have not read anything like this in reference books, but was just giving free thoughts.