bet you thought you were done with the pumpinglemma.3a. [10 points] SupposeLis a regular language, and letpbe its pumping length. Prove thatLis infinite iffLcontains a string whose length is?pand

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3. [20 points I bet you thought you were done with the pumping lemma 3a. [10 points] Suppose L is a regular language, and let p be its pumping length. Prove that L is infinite iff L contains a string whose length is-p and 2p. 3b. [10 points We saw in class that ADFA and EDFA are decidable. Now show that FDFA M) : M is a DFA and L(M) is finite} is decidable, by using part 3a. (By the way, the same approach works to show that FpDa is decidable, using the pumping lemma for context-free languages, which we unfortunately didn't have time to cover this semester.)