16. Construct a PDA accepting L by empty store where L = {a'b"a" |n21, j20 17. Construct a PDA accepting {a'b"c" :n 21, j21} by final state. 18. Constuct a CFG generating {a"b" | n21} {a" ,2 m2 1}. Using this CFG, construct a PDA accepting the given set by empty store. 19. Using Pumping lemma show that the language L = {a'b'c|i20} is not context free. 20. Using Pumping lemma show that the language L = {a" "cP10 smsnsp is not a CFL. 21. Using Pumping Lemma prove that the language L = {www {0,1) is not a CFL. 22. Consider the set of all strings over {a,b) with no more than twice as many a's as b's: {xe{a, b" | # a(x)= 2# b(x); (a) Give a CFG for this set, and prove that it is correct. (b) Give a PDA for this set. Show sample runs on the input strings aabbaa, aaabbb and aaabaa. 23. Consider the set a*bc* {a"6"c" |n 20} the set of all strings of a's followed by b's followed by c's such that the number of a's, b's and c's are not all equal. (a) Give a CFG for the set, and prove that your grammar is correct. (b) Give an equivalent PDA. 24. Show that {a,b}" {a"b" | n20} is not context free