Re: The Modified Halting Problem, Take ??? .

The Ghost In The Machine wrote:
I. The Claim.

The claim has been made that the following, or a variant
thereof, is an ill-formed question. [*]

Given a codestring S and a parameter-array A, determine
whether the lambda-call S(A) will return a result in
a finite amount of time, or endlessly loop.

I for one dispute that claim, although one might ask what
a codestring is, as the original was done more rigorously
through a Turing-machine system, which had a state set,
a transition function, a start state, and one or more
halting-states. (I consider my way simpler, and more in
line with current coding practices; it shouldn't matter,
though.)



A Possible Solution to the Modified Halting Problem, Give or Take

Diplomat that I am, I believe I have found an amicable
resolution to the conflict between Peter Olcott and
R. Srinivasan which neatly ties up all the debate's loose ends:

R. Srinivasan wrote:

> Is this a naive philosophical viewpoint? Maybe or maybe not. If you
> know any open-minded philosophers or logicians who are willing to
> discuss NAFL with me and help me polish up the arguments, please do
> let me know.
>

Yes! I found one, he arrives at a similar conclusion, regarding
Cantor and then Turing's impact on Hilbert's program but maybe
you guys can iron out any kinks in your approaches and mutualize.


http://math.nist.gov/mcsd/Seminars/2002/2002-11-12-engel.html

Turing computability and related topics re-visited by Joe Engel

Abstract: 1) "A Comprehensive Turing Machine may be defined as one
that will print a well ordered set of Turing Tapes containing every
Tape that begins with any possible ordered set of 0's and 1's of any
given finite length n when operating on any given initial computable
tape of indefinite (infinite) length. Such Machines exist. The same
CTM operating on any initial infinitely long computable tape prints
a well ordered denumerably infinite set of all Computable Turing Tapes.
2) There is no halting problem. This is accomplished by defining any
putative CTM that jams as a defective machine. Such a machine is
redundant, in any case, since it will print, before it halts, only
tapes that can be produced by any valid Comprehensive Turing Machine.
Taken together these results have caused me to re-examine Turing's
demonstration of the unsolvability of Hilbert's problem, as well as
Cantor's demonstration of the existence of non denumerable sets.
NEITHER OF THE ABOVE RESULTS IS OBVIOUS. HOW THESE RESULTS WERE
ARRIVED AT WILL BE DISCUSSED BRIEFLY DURING THIS PRESENTATION."

Glad to be of service,
Stephen

.

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