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Peter Linz Edition 5 Exercise 12.4 Question 2 (Page No. 321)
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Show that the problem of determining whether or not $L(G_1) \subseteq L(G_2)$ is undecidable for context-free grammars $G_1,\space G_2$.
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Peter Linz Edition 5 Exercise 12.4 Question 8 (Page No. 321)
Let $G_1$ and $G_2$ be grammars with $G_1$ regular. Is the problem $L(G_1) = L(G_2)$ decidable when $\text(a)$ $G_2$ is unrestricted, $\text(b)$ when $G_2$ is context-free, $\text(c)$ when $G_2$ is regular$?$
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Peter Linz Edition 5 Exercise 12.4 Question 7 (Page No. 321)
Let $G_1$ be a context-free grammar and $G_2$ a regular grammar. Is the problem $L(G_1)\cap L(G_2) = \phi$ decidable$?$
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Peter Linz Edition 5 Exercise 12.4 Question 6 (Page No. 321)
Let $M$ be any Turing machine. We can assume without loss of generality that every computation involves an even number of moves. For any such computation $q_0w\vdash x_1\vdash x_2\vdash ...\vdash x_n$, we can then construct the string ... to show that $ L(G) = \Sigma^* $ is undecidable over the domain of all context-free grammars G.
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Peter Linz Edition 5 Exercise 12.4 Question 5 (Page No. 321)
Let $L_1$ be a regular language and $G$ a context-free grammar. Show that the problem $“L_1 \subseteq L(G)”$ is undecidable.
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