Can every linear grammar be converted to Greibach form?

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.)

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.

EDIT: the rest of this answer is out of scope since the question was about Linear GNF and not just GNF (thanks @hendrik-jan for spotting this)

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).

StackExchange Computer Science Q#588, answer score: 9