Yeah, no.
That Barret M82 chambered in .50 BMG I was talking about, I don't need a "permit" I just have to be 21, have the money, and fill out the paperwork for a background check and to get the gun in my name.
Now, a fully-automatic weapon requires a Class 3 machine gun license which you have to register with the ATF and they drop in once a month to check on said weapon.
My friend's sister is a nurse in the army and she own three or two AK-47s, but this is in Nevada or Arkansas (however you spell it)