Ullman (TOC) Edition 3 Exercise 7.1 Question 6 (Page No. 278)

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Ullman (TOC) Edition 3 Exercise 7.1 Question 11 (Page No. 278 - 279)
In this exercise, we shall show that for every context-free language $L$ containing at least one string other than $\in,$there is a $CFG$ in Greibach normal form that generates $L-\in.$ Recall that a Greibach normal form $(GNF)$ grammar is ... $(a).$ Then fi x the $B_{i}$ productions in any order , again $(a).$

In this exercise, we shall show that for every context-free language $L$ containing at least one string other than $\in,$there is a $CFG$ in Greibach normal form that gen...

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Ullman (TOC) Edition 3 Exercise 7.1 Question 10 (Page No. 278)
Is it possible to find, for every context-free language without $\in,$ a grammar such that all its productions are either of the form $A\rightarrow BCD$ $($i.e., a body consisting of three variables$),$ or $A\rightarrow a$ $($i.e., a body consisting of a single terminal$)?$ Give either a proof or a counterexample.

Is it possible to find, for every context-free language without $\in,$ a grammar such that all its productions are either of the form $A\rightarrow BCD$ $($i.e., a body ...

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Ullman (TOC) Edition 3 Exercise 7.1 Question 9 (Page No. 278)
Provide the inductive proofs needed to complete the following theorems$:$ The part of Theorem $7.4$ where we show that discovered symbols really are generating. Both directions of Theorem $7.6$ where we show the correctness of ... reachable symbols. The part of Theorem $7.11$ where we show that all pairs discovered really are unit pairs.

Provide the inductive proofs needed to complete the following theorems$:$ The part of Theorem $7.4$ where we show that discovered symbols really are generating.Both direc...

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Ullman (TOC) Edition 3 Exercise 7.1 Question 8 (Page No. 278)
Let $G$ be an $\in-$production-free grammar whose total length of production bodies is $n.$ We convert $G$ to $CNF.$ Show that the CNF grammar has at most $O(n^{2})$ productions. Show that it is ... $n^{2}.$ Hint$:$Consider the construction that eliminates unit productions.

Let $G$ be an $\in-$production-free grammar whose total length of production bodies is $n.$ We convert $G$ to $CNF.$Show that the CNF grammar has at most $O(n^{2})$ produ...

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Ullman (TOC) Edition 3 Exercise 7.1 Question 6 (Page No. 278)

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