constructing CFG

Question

How can I construct a Context-Free Grammer for the language x^a y^b z^2(a+b) where a>=0, b>=0. Thanks for helps...

Answer 1

Think of it this way

x^a y^b z^2(a+b) = x^a y^b z^2a z^2b = x^a y^b (z^2)^b (z^2)^a 

Therefore

S -> xSzz | S1
S1 -> yS1zz | e