2. Let us consider the language of algebraic expression, ALEX, defined by the recursive definition on p. 29. We never attempted to give a regular expression for this language because it is nonregular. Prove this using the Myhill-Nerode theorem and the sequence (x (Ox (Ox 13. Define the language MOREA as follows: MOREA = (all strings of a's and b's in which the total number of a's is greater than the total number of b's) ={a aa aab aba baa aaab aaba ) (i) Use the fact that MOREA, n MOREB, n (a + b)" EQUAL to prove that MOREA is nonregular (where MOREB has its obvious meaning). lar by using the sequence (ii) Explain why the pumping lemma cannot be used to prove that MOREA is nonregu- (ii) Show that MOREA can be shown to be nonregular by the Myhill-Nerode theorem 2. Let us consider the language of algebraic expression, ALEX, defined by the recursive definition on p. 29. We never attempted to give a regular expression for this language because it is nonregular. Prove this using the Myhill-Nerode theorem and the sequence (x (Ox (Ox 13. Define the language MOREA as follows: MOREA = (all strings of a's and b's in which the total number of a's is greater than the total number of b's) ={a aa aab aba baa aaab aaba ) (i) Use the fact that MOREA, n MOREB, n (a + b)" EQUAL to prove that MOREA is nonregular (where MOREB has its obvious meaning). lar by using the sequence (ii) Explain why the pumping lemma cannot be used to prove that MOREA is nonregu- (ii) Show that MOREA can be shown to be nonregular by the Myhill-Nerode theorem