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Say that a variable $A$ in $CFG \:G$ is necessary if it appears in every derivation of some string $w \in G$. Let $NECESSARY_{CFG} = \{\langle G, A\rangle \mid \text{A is a necessary variable in G}\}$.

  1. Show that $NECESSARY_{CFG}$ is Turing-recognizable.
  2. Show that $NECESSARY_{CFG} $is undecidable.
in Theory of Computation by Veteran (59.2k points)
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