# Peter Linz Edition 5 Exercise 12.2 Question 4 (Page No. 311)

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Let $G$ be an unrestricted grammar. Does there exist an algorithm for determining whether or not $L(G)^R$ is recursive enumerable$?$

## Related questions

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For an unrestricted grammar $G$, show that the question $“Is \space L(G) = L(G)^*?”$ is undecidable. Argue $\text(a)$ from Rice’s theorem and $\text(b)$ from first principles.
Let $G_1$ be an unrestricted grammar, and $G_2$ any regular grammar. Show that the problem $L(G_1) \space\cap L(G_2) = \phi$ is undecidable for any fixed $G_2,$ as long as $L(G_2)$ is not empty.
Let $G_1$ be an unrestricted grammar, and $G_2$ any regular grammar. Show that the problem $L(G_1) \space\cap L(G_2) = \phi$ is undecidable.
Let $G$ be an unrestricted grammar. Does there exist an algorithm for determining whether or not $L(G) = L(G)^R$?\$