A language L is regular if it is recognized by a finite automaton, i.e., the automaton finishes in an accepting state if and only if the input is in the language L. A string y is a prefix of x if there exists a string z with x = yz. A string y is a substring of x if there exist strings w and z with x = wyz. For a string over the alphabet = {0,1}, let #(a,x) be the number of times a substring aa occurs in the string x. Different aa strings are allowed to overlap. For example, #(0,00111001) = #(1,00111001) = 2. (a) Define L = {2 | #(0,y) = #(1, y) for all prefixes y of x}. Give an informal argument, why this language L is not regular, or draw a transition diagram of a finite automaton accepting L. (b) Define L' = L n {x| #(1, y)