Berman's theorem states
If a unary language ( a language with all the strings of the type $1^i$, $ i > 0 $ ) is NP-Complete then P = NP.
I tried reducing SAT to a given unary language $L$ assuming it is NP-Complete. But I can't think of a way such that after applying the reduction so that SAT gets solved in polynomial time. How do I proceed further?
This is an exercise from Sanjeev Arora and Boaz Barak , but not homework.