Given any strings u and z (with u ∈ Σ*), define #uz to be the number of times u occurs as a substring of z. For example, if u = 010 and z = 01010, then #uz = 2 because two occurrences are counted even though they overlap. Using the Myhill-Nerode technique (not the Pumping Lemma), prove that two of the following languages are not regular and give a regular expression for the one that is regular.
aL = {z ∈ {0,1}* : #00 > #11}
bL = {x ∈ {0,1}* : #01z > #10x}
cL = {0y#0 = #1y}