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gwern comments on Open thread, August 5-11, 2013 - Less Wrong
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Already tested by Light in the manga, IIRC; the limits of skill top out before things like 'escape from maximum-security prison', so P=NP is well beyond the doable.
Ah, I've only seen the anime.
I'd also try "The person will die of cause A if X is true, and cause B if X is false" and other ways to try to push the burden of skill onto whatever mysterious universal forces are working instead of the human.
He tries it in the anime too. (I watched that episode yesterday.) He tries things like "draw a picture of L on your cell wall and then die of a heart attack" on some evil prisoner. It doesn't work.
That's clever, and should be tried.
It might even be possible to jam up the system with a sufficiently hard to compute death requirement, though I'm not sure I'd want to try it. The death note is rather valuable.