3 a,b,c

T = (3) Prove that the following three languages are non-regular via the Myhill-Nerode Theorem. All use alphabet & = {0,1}. Here xR stands for x reversed, e.g. 0111R 1110. The condition = XR means that x is a palindrome, but the members of La are a little more restrictive, including 1001 but not 10001. For Lc, be careful that if you leave out any trailing zeroes in your strings xz or yz," that counts as having k = 0. (3 x 12 = 36 pts., for 74 total on the set) (a) La = {":2 *}. (b) b = {r E I* : #0(2) > #1(x)}. (C) L3 = {0*130*: i=j or i #k (i, j, k > 0)}. T = (3) Prove that the following three languages are non-regular via the Myhill-Nerode Theorem. All use alphabet & = {0,1}. Here xR stands for x reversed, e.g. 0111R 1110. The condition = XR means that x is a palindrome, but the members of La are a little more restrictive, including 1001 but not 10001. For Lc, be careful that if you leave out any trailing zeroes in your strings xz or yz," that counts as having k = 0. (3 x 12 = 36 pts., for 74 total on the set) (a) La = {":2 *}. (b) b = {r E I* : #0(2) > #1(x)}. (C) L3 = {0*130*: i=j or i #k (i, j, k > 0)}