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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

  • $S \rightarrow aYc$
  • $Y \rightarrow a Yc\mid Q$
  • $Qc \rightarrow Rc$
  • $cR \rightarrow Rc$
  • $aR \rightarrow a - Q$
  • $bR \rightarrow b - Q$
  • $Qb \rightarrow ...$
  • $Qc \rightarrow cQ$
  • $Q \rightarrow R'c$
  • $cR' \rightarrow ...$
  • $bR' \rightarrow ...$
  • $aR' \rightarrow a...$
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