Peter Linz Edition 4 Exercise 5.1 Question 19 (Page No. 134)

Question

Show a derivation tree for the string $aabbbb$ with the grammar

$S\rightarrow AB|\lambda,$

$A\rightarrow aB,$

$B\rightarrow Sb.$

Give a verbal description of the language generated by this grammar.

Answer 1

here derivation tree is easy to draw AB→ ASb →  Ab →  aBb →  aSbb→  aABbb→  aASbbb→  aAbbb →  aaBbbb→  aaSbbbb → aabbbb 

and the language is like this 2na(v)  >= nb(v)  where v is  any prefix in w belongs to L

correct if i am wrong.