I have a language $ L= \{ w \in \{a,b\}^* ; |w|_b=2i, i \ge 0 \}$ that is a language with even number of b's.
I found a grammar for it with these rules:
$S \rightarrow aS \ | \ bL \ | \ \lambda $
$L \rightarrow aL \ | \ bS \ $
How could I show that this language cannot be generated by linear grammar?
According to Wikipedia, a linear grammar is a context-free grammar that has at most one nonterminal in the right hand side of its productions.