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gwern comments on What independence between ZFC and P vs NP would imply - Less Wrong Discussion

1 Post author: alexflint 08 December 2011 02:30PM

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Comment author: gwern 08 December 2011 08:09:44PM 1 point [-]

That would only work for some turing machines. Incidentally, it's perfectly possible to decide for particular finite turing machines whether it halts - basically either set a time-out equivalent to the Busy Beaver for that TM (and it either halts before, or blows the time-out in which case it never halts), or, IIRC, you can store every configuration of the tape it passes through and if it repeats any configuration, then it will not halt. Neither of these is especially useful.

Comment author: dlthomas 08 December 2011 08:17:43PM 2 points [-]

That would only work for some turing machines.

Of course. I made no claim at having solved the halting problem. My response was specifically to,

what empirical data could prove that it halts eventually, other than seeing it halt?

There is nothing else that will reliably show this for all machines. There are absolutely things that will show this for some machines.