For arbitrary strings x and y, we define #_y(x) to be | {(u,v) : x = uyv } |.

Let = {2,4}.

Let L₁ = {x * : #₂₄(x) = 2. #₄₂(x)}.

Nick created a CFG that generates L₁, but before he showed it to anyone, an error occurred

Three productions were deleted, leaving blanks where they were. Here is what's left of Nick's CFG.

• S -> blank1, blank2, blank3
• A -> 2A,
• B -> 4B,

Complete Nick's CFG by giving values for the blanks.