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Michael Sipser Edition 3 Exercise 1 Question 65 (Page No. 93)

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Prove that for each $n > 0,$ a language $B_{n}$ exists where

  1. $B_{n}$ is recognizable by an $\text{NFA}$ that has $n$ states, and
  2. if $B_{n} = A_{1}\cup...\cup A_{k},$ for regular languages $A_{i},$ then at least one of the $A_{i}$ requires a $\text{DFA}$ with exponentially many states$.$
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Michael Sipser Edition 3 Exercise 1 Question 71 (Page No. 93)
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Michael Sipser Edition 3 Exercise 1 Question 69 (Page No. 93)
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