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The logic of pumping lemma is a good example of

  1. the pigeon-hole principle
  2. the divide and conquer technique
  3. recursion
  4. iteration
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A

Explanation: pigeon hole principle states that, if we have n objects & m boxes s.t. #objects > #boxes & we are required to put ever object in a box, then at least 1 box will contain more than 2 objects.

this same principle applies for pumping lemma in a bit different form.

if a string of length n need to be accepted by a FA then it require at least n+1 states. Now if this string have some part repeating then we may have to apply loop on at least 1 state. 

Answer:

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The open-loop transfer function of a feedback control system is $G(s)\cdot H(s) = 1/(s+1)^{3}.$ The gain margin of the system is $2$$4$$8$$16$