Consider the following type 0 grammar over the alphabet = {a}. (i) Draw the total language

Question:

Consider the following type 0 grammar over the alphabet Σ = {a}.

(i) Draw the total language tree of this language to find all words of five or fewer letters generated by this grammar.
(ii) Generate the word a9 = aaaaaaaaa.
(iii) Show that for any n = 1, 2, . . . , we can derive the working string

AnBnD

(iv) From AnBnD. show that we can derive the working string

an2BnAnD

(v) Show that the working string in part (iv) generates the word

a(n+1)2

(vi) Show that the language of this grammar is

SQUARE = {an2 where n = 1 2 3 . . .}

= {a aaaa a9 a16 • • •}

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