Re: Extramathematical Notions and the Continuum Hypothesis -- Correction

Peircers,

The FOM List moderators have kindly corrected my previous statement:
The truth is that computable functions are NOT ultimately periodic.
Digging up an old textbook -- this seems to be a good day for that --
it seems that my memory slipped a cog from the very special case
of “deterministic finite-state automata” to the general case of
Turing machines.  Here is probably the text I had in mind:

| 6.4.  Ultimately Periodic Behavior
|
| We shall show that the response of a deterministic transducer to an ultimately periodic input
| must be ultimately periodic.  The proof of the result is analogous to the proof of Theorem 6.3:
| we construct a generator for the ultimately periodic input, form the cascade combination of the
| generator and the given transducer, and demonstrate that the resulting machine is a generator for
| an ultimately periodic output.  To do this, we first show that ultimately periodic strings are
| precisely the strings generated by deterministic finite-state generators.
|
| Denning, P.J., Dennis, J.B., and Qualitz, J.E. (1978), _Machines, Languages, and Computation_,
| Prentice-Hall, Englewood Cliffs, NJ, p. 213.

I will have to think on that a while ...

Regards,

Jon

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