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Re: Halting Undecidability proof faulty?
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Originally Posted by alexander
3 states 2 colors... sounds like a quantum computing device, though there you may not refer to them as colors, but more of polarities or directions... This would be neat for storage, we would tripple the capacity of the same size storage device if we were able to store in it using 6 state qbit system even quadruple with an 8 state qbit system... also access speed would increase, because they would have to accomodate the 8 states, you will now be able to write 4 times more efficiently then with binary over the same speed bus, all those minutes you spent learning octal would not have been spent for nothing  |
Hi Alexander,
Unfortunately the relationship between states and colors means that less colors require more states for a Universal Turing Machine.
Universal Turing Machine -- from Wolfram MathWorld
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A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave the first construction for a universal Turing machine (Turing 1937, 1938). Shannon (1956) showed that two colors were sufficient, so long as enough states were used. Minsky (1962) discovered a 7-state 4-color universal Turing machine, illustrated above (Wolfram 2002, p. 706). Note that the 20th rule specifies that the Turing machine should halt, as indicated by leaving the head stationary and not changing its state. Upon conversion to a 2-color machine, Minsky's universal Turing machine requires 43 states.
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Corollary to the Peter Principle: Once you have promoted all of your competents to their highest level of incompetence you must change your management philosophy from top down to bottom up, because the staff at the bottom are the only competent ones in your entire organisation.
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