It is possible to define the term simplification precisely by introducing the concept of complexity of a grammar. This can be done in many ways; one of them is through the length of all the strings giving the production rules.
For example, we might use
$complexity(G)=$$\sum_{A\rightarrow V ∈ P}${$1+|v|$}
Show that the removal of useless productions always reduces the complexity in this sense. What can you say about the removal of $λ$-productions and unit-productions?
