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Peter Linz Edition 5 Exercise 11.2 Question 1 (Page No. 290)
Rishi yadav
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What language does the unrestricted grammar
$S\rightarrow S_1B,$
$S_1\rightarrow aS_1b,$
$bB\rightarrow bbbB,$
$aS_1b\rightarrow aa,$
$B\rightarrow \lambda$
derive$?$
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Peter Linz Edition 5 Exercise 11.2 Question 9 (Page No. 290,291)
A grammar $G = (V, T, S, P)$ is called $\text{unrestricted }$ if all the production are of the form $u\rightarrow v$, where $u$ is nit $(V\cup T)^+$ and $v$ is int $(V\cup T)^*$ Some authors give ... the same as the one we use, in the sense that for every grammar of one type, there is an equivalent grammar of the other type.
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Peter Linz Edition 5 Exercise 11.2 Question 8 (Page No. 290)
Every unrestricted grammar there exists an equivalent unrestricted grammar, all of whose productions have the form $u\rightarrow v,$ with $u,v\in (V \cup T)^+$ and $|u| \leq |v|$, or $A\rightarrow\lambda$ with $A\in V$ Show that the conclusion still holds if we add the further conditions $|u|\leq2$ and $|v|\leq2$
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Peter Linz Edition 5 Exercise 11.2 Question 7 (Page No. 290)
Show that for every unrestricted grammar there exists an equivalent unrestricted grammar, all of whose productions have the form $u\rightarrow v,$ with $u,v\in (V \cup T)^+$ and $|u| \leq |v|$, or $A\rightarrow\lambda$ with $A\in V$
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Peter Linz Edition 5 Exercise 11.2 Question 6 (Page No. 290)
$\text{Theorem}:$ For every recursively enumerable language $L$, there exists an unrestricted grammar $G$, such that $L=L(G)$. Construct a Turing machine for $L(01(01)^*)$, then find an unrestricted grammar for it using the construction in Theorem. Give a derivation for $0101$ using the resulting grammar.
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