Theory of Computations 6. Prove (L*)* = L* for all languages L.

7. Let L be a finite language on {a}*. Is Ln for some arbitrary integer n finite or infinite? Justify your answer.

8. For = {a, b}, construct a dfa that accepts the set of all strings containing exactly one a.

9. Let = {a}. Show that the language L = {w: w *, |w| 0, but |w| 4} is regular.

10. Which of the strings 0001, 01001, 0000110 are accepted by the dfa on the back.

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