Describe a context free grammar for the following language i

Describe a context free grammar for the following language.

i,j0 & L

L = {0^i 1^j 2^k| k = 2(i + j)}

Prove that L is context free by describing a grammar for L.

Prove that your grammar is correct. You need to prove that if L L(G) and L(G) L where G is your grammar from the previous part.

Solution

G = (V, , R, S) through set of variables V = {S, X},

Here S is the start variable

Set of terminals = {a, b, c}

Rules

S 0S2 | X

X 1X2 |