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Peter Linz Edition 4 Exercise 5.1 Question 25 (Page No. 135)
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Prove that if $G$ is a context-free grammar, then every $w ∈ L(G)$ has a leftmost and rightmost derivation. Give an algorithm for finding such derivations from a derivation tree.
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Peter Linz Edition 4 Exercise 5.1 Question 26 (Page No. 135)
Find a linear grammar for the language $L=$ {$a^nb^m:n\neq m$}.
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Peter Linz Edition 4 Exercise 5.1 Question 27 (Page No. 135)
Let $G = (V,T,S,P)$ be a context-free grammar such that every one of its productions is of the form $A → v,$ with $|v| = k > 1.$ Show that the derivation tree for any $w ∈ L(G)$ has a height $h$ such that $\log_{k}|w|\leq h\leq \frac{(|w|-1)}{k-1}$.
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Peter Linz Edition 4 Exercise 5.1 Question 24 (Page No. 135)
Find a context-free grammar that can generate all the production rules for context-free grammars with $T =$ {$a, b$} and $V =$ {$A, B, C$}.
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Peter Linz Edition 4 Exercise 5.1 Question 23 (Page No. 135)
Find a context-free grammar for the set of all regular expressions on the alphabet {$a, b$}.
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