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Someone had to say it: Scientists propose AI apocalypse kill switches
(www.theregister.com)
This is a most excellent place for technology news and articles.
I think it was in the matrix where humans nuked a bunch of stuff to kick up enough dirt to block out the sun (the robots were solar powered)
The robots still figured out how to survive...
I'm sure a sufficiently advanced AI could build a backup power source or trick a human into doing it