From: Dan Fabulich (daniel.fabulich@yale.edu)
Date: Thu Dec 14 2000 - 14:45:06 MST
John Clark wrote:
> >If a thermostat can alter its own settings, then it is infinite-state by definition.
> What a silly thing to say, it's infinite-state by definition if it
> has infinite states. If a finite state Turing machine can't alter
> its own settings then you should be able to predict what it will do,
> so I'll run one programmed to look at the even numbers greater than
> 4 and stop when it finds the first on that is that is not the sum of
> two primes (except 1 and 2). It's a simple program needing just a
> few lines of code, but will it ever stop? Nobody knows, and it's
> entirely possible nobody will ever know because its unknowable even
> in theory.
Wellll... If it only has a finite amount of tape, and it halts when
it runs out of tape, you should be able to figure it out. Without an
infinite amount of tape, it'll be unable to store the next number in
memory.
Hopefully your machine is set to halt if/when it runs out of tape.
But if not, it'll presumably just wrap around (like what happens when
you add 0x01 to 0xFF) or do some other predictable thing. Then you
really *CAN* tell if it'll halt or not.
-Dan
-unless you love someone-
-nothing else makes any sense-
e.e. cummings
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