3. (10 - basics) (Foundation) Study the pumping lemma.
(a) List all concepts used in the lemma. Each concept should be in the format of concept name and arguments of the concept.
(b) List all logical symbols used in the lemma.
4. (10 - medium) (Ideas underlying Pumping Lemma) Given an NFA M and a computation over it: (p1,abc) -m (p2,bc) Fm (p2,c) m (p3,e) where pi is the start state and p3 a final state. (Hint. Not only recall what accept intuitively means, but also its formal definition. Note also the repetition of state p2 in the computation.)
(a) is string abc accepted by M? (b) is string ac accepted by M? (c) is string ab'c accepted by M? (d) Explain why for any non-negative number n, ab"c is accepted by M?
CS3383 Theory of Automata by Y Zhang, TTU, Fall 2022
5. (5 - advanced) (Comprehensive). Using pumping lemma, prove the language {0^n1^n | n >= 0} over alphabet E = {0, 1} is not regular.