Answer Happy

Question 2 Prove by contradiction that the following language is not regular. (5 marks) L2 = {0"1":nm, n > 0,m>0} . Do NOT use the Pumping Lemma. Instead, make use of closure properties of operations on regular languages, and make use of the fact that the language A = {0"1" : n>0} is not regular (proven in Lecture 12). Question 3 (2 marks) Is the following language over Σ = {0, 1} regular or not? Prove your answer. L3 = {w: the substring 01 occurs exactly as often in w as the substring 10} (An example of a string in the language is 010 because there is one occurrence of the substring 01 and one occurrence of the substring 10. An example of a string NOT in the language is 0101 because there are two occurrences of the substring 01 but only one occurrence of the substring 10.)