1b) Let A = {aibjck∶0 ≤ i ≤ j ≤ k}. Use the pumping lemma for context-free languages to prove that A is not a context-free language.

Write in the space below the statement of the pumping lemma for context-free languages. Then use it to show that the following language is not context free {ambnam|n>m+1>0} Pumping Lemma Statement:

1. Show that the following language on E= {a, b, c} is not context free using pumping lemma for context free languages. L = {a"b°c*: k> n, k>j}

55. Find a deterministic finite-state automaton that recog- nizes each of these sets. b) {1, 00} a) {0} c) {1" | n = 2, 3, 4, ...} 56. Find a nondeterministic finite-state automaton that recog- nizes each of the languages in Exercise 55, and has fewer states, if possible, than the deterministic automaton you found in that exercise.