The context free grammar for the language $L= \left\{a^{n}b^{m}c^{k} \mid k = \mid n - m\mid , n \geq 0, m \geq 0, k \geq 0\right\}$ is
- $S \rightarrow S_{1}S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
- $S \rightarrow S_{1}S_{3}, S_{1} \rightarrow aS_{1}S_{2}c \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
- $S \rightarrow S_{1} \mid S_{2}, S_{1} \rightarrow aS_{1}S_{2}c \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$
- $S \rightarrow S_{1} \mid S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b\mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda$