Solve c

! Exercise 4.1.2: Prove that the following are not regular languages. * a) {0| n is a perfect square}. b) {ON | n is a perfect cube}. c) {0" | n is a power of 2}. d) The set of strings of O's and 1's whose length is a perfect square. e) The set of strings of O's and ls that are of the form ww, that is, some string repeated. f) The set of strings of O's and i's that are of the form ww, that is, some string followed by its reverse. (See Section 4.2.2 for a formal definition of the reversal of a string.) g) The set of strings of O's and l's of the form ww, where w is formed from w by replacing all O's by l's, and vice-versa; e.g., 011 = 100, and 011100 is an example of a string in the language. h) The set of strings of the form w1", where w is a string of O's and l's of length n