Question

Let . Show that$\mathit{A}{\mathit{\epsilon }}_{\mathbf{\text{CFG}}}$is decidable.

Short answer

It can be shown that $A{\epsilon }_{\text{CFG}}$is decidable.

Step-by-step solution

Explain context-free grammar

Context-free grammar generates the context-free languages by using the production rules. The context-free grammars has the productions that has the variables and terminals.

Show that AεCFG is decidable

Convert the context-free grammar$G$ into an equivalent$G\text{'}$ CNF that is represented by the Turing machine $S$. Construct the Turing machine$M$ that decides $A{\epsilon }_{\text{CFG}}$.

where$G$ is a context-free grammar.

1. Run the Turing machine $S$on input , where $A{\epsilon }_{\text{CFG}}$is decided by the Turing Machine $S$.
2. If $S$accepts, accept.
3. If$S$ rejects, reject.

Therefore, It has been shown that $A{\epsilon }_{\text{CFG}}$is decidable.