Q15b

Complete the following production rules which generate the language:

$$L= \left\{a^{n} b^{n} c^{n}\mid a, b, c \in \Sigma \right\}$$

where variables $R$ and $Q$ are used to move back and forth over the current string generated $S \rightarrow aYc$ $Y \rightarrow a Yc\mid Q$ $Qc \rightarrow Rc$ $cR \rightarrow Rc$ $aR \rightarrow a - Q$ $bR \rightarrow b - Q$ $Qb \rightarrow ...$ $Qc \rightarrow cQ$ $Q \rightarrow R'c$ $cR' \rightarrow ...$ $bR' \rightarrow ...$ $aR' \rightarrow a...$