Can a non-deterministic Turing machine accurately simulate a deterministic one? If not, how much redundancy would be needed to be 99.999% certain that an error would not occur under standard operating conditions within the universe's life span?
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Anonymous2014-07-14 15:15
Turing machines don't exist. Your question is useless. Better off discussing elves and pixies.
Let c be the chance that a NDTM compute unit will produce an incorrect result. Let T be the time in seconds until the death of the universe. Let n be the count of NDTM compute units. Let X be a random variable signifying the length of time before failure. Let p = c(n/2-1), the probability that more than half of the compute units return an incorrect result. Let g be the number of operations, during which a compute unit may return an incorrect result, performed per second. Let N = ngT, the total operations performed. Let L = Nc, the expected number of incorrect results returned.
Assume all the assumptions of a Poisson process.
Note that P(X>T)=P(X(t)=0)=e-Lt 0.99999=e-cngT -ln(0.99999)/cgT=n
There will be no death of the universe. There isn't even an accepted consensus about the fate of the universe, it being finite or infinite, or whatever. negative atheists should all kill themselves
>>10 I'm sorry, I didn't realize that the ABSTRACT BULLSHITE statistical distribution most correlated with things like radioactive decay and nonsensical garbage like that wouldn't be applicable to real-world things like machines with an infinitely long tape running for the rest of eternity.