Is there a regular grammar for the language $\{ w : |w|_0 = |w|_1 \}$? I need to prove whether the language $ L = \{w \in \{0,1\}^* \mid |w|_0 = |w|_1 \}$ can be written as a regular grammar. Obviously it can, but how do I prove it?
A language can be described by a regular grammar if and only if it is regular. Your language is nor regular, hence it cannot be described as a regular grammar.