context free grammar

Question

Construct context-free grammars to accept the following languages.

$$\begin{align*} \large L = \left \{ 0^i1^j2^k \;\; | \;\; i \neq j \;\; or \;\; j \neq k \right \} \end{align*}$$

Answer 1

$$\begin{align*} &S\rightarrow S_1 \;\; | \;\; S_2 \\ \\ &S_1 \rightarrow ABD \;\; | \;\; CAD \\ \\ &A \rightarrow 0A1 \;\; | \;\; \epsilon \\ \\ &B \rightarrow 1B \;\; | \;\; 1 \\ &C \rightarrow 0C \;\; | \;\; 0 \\ &D \rightarrow 2D \;\; | \;\; \epsilon \\ \\ &S_2 \rightarrow GEF \;\; | \;\; GBE \\ \\ &E \rightarrow 1E2 \;\; | \;\; \epsilon \\ &F \rightarrow 2F \;\; | \;\; 2 \\ &G \rightarrow 0G \;\; | \;\; \epsilon \\ \end{align*}$$

Comments

thnq debashish da

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how to write it for L = {0^i1^j2^k : I != j and j!=k}