Can every linear grammar be converted to a linear Greibach normal form, a form in which all productions look like $A \rightarrow ax$ where $a \in T$ and $x \in V \cup \{\lambda\}$?($T$ is the set of terminals, $V$ is the set of non-terminals, $\lambda$ is the empty sequence.)
Can every linear grammar be converted to Greibach form?
formal languages;formal grammars
The more general answer is:Blum and Koch showed a polynomial time transformation such that any context-free grammar can be converted to Greibach form.Since a linear grammar is a special case of Context-free grammar, the answer is yes.A simpler transformation:Any rule $X \rightarrow a_1 a_2 \cdot a_k Y$ you transform them in $k$ rules: $X\rightarrow a_1 X_1Y$.$\cdots$$X_{i-1}\rightarrow a_{i}X_i$$X_{k-1}\rightarrow a_{k}Y$Any rule $X \rightarrow a Y b$ should be transformed in two rules$X \rightarrow a Y Y_1$.$Y_1 \rightarrow b$where the capital letters belong to $V$ and the small letters to the alphabet (terminals).