1. Let G be a context-independent grammar whose rule set is as follows: S ASB I A aA I B bB I a. Give a left derivation and a right derivation of the word aaabb. b. Construct the derivation tree from any of the above derivations. c. Prove that G is ambiguous. d. Construct an unambiguous grammar equivalent to G. e. Describe L(G). Is this language regular?

Derivation on the left 1 2 2 2 2.1 1.1 3 3 3.1 AASB aa ASB aaaASB aaaSB aaabb aaabbb S ASB aaabb Derivation on the right 3 3 3.1 1.1 2 2 2 2.1 S ASB ASbbB ASbb Abb aAbb aaAbb aaaAbb aaabb w WAMA Derivacin izquierda ab S A A SB a A E b B Derivacin derecha ab E S E Derivacin izquierda ab A S B S a A E b B A A S B E E a A ASB b B E E