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L={${a^{n^{2}}/n\geq 0}^{\ast }$}$^{\bigstar }$ find machine which accept
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Since there is a * waiting outside, putting n = 1 gives the string $a^1$ which is $a$. Now use your friend *, the one who is waiting for you outside. So it will generate every string over the unary alphabet as the language generated will be $a^*$. So the machine accepting $a^*$ needs only 1 state.
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