From Newsgroup: comp.lang.c
On 10/14/2022 7:44 PM, Ben Bacarisse wrote:
*Original context*
On 10/14/2022 12:06 PM, olcott wrote:
Professor Sipser has agreed that this is the correct criteria:
If simulating halt decider H correctly simulates
its input D until H correctly determines that its
simulated D would never stop running unless aborted then
H can abort its simulation of D and correctly report
that D specifies a non-halting sequence of configurations.
I don't think that is the shell game. PO really
/has/ an H (it's trivial to do for this one case)
that correctly determines that P(P) *would* never
stop running *unless* aborted.
He knows and accepts that P(P) actually does stop.
The wrong answer is justified by what would
happen if H (and hence a different P) where not
what they actually are.
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
After many very extensive discussions with LLM
systems there are two principles that prove that
I have correctly refuted the halting problem itself.
(1) the behavior that an input DD specifies to a
halt decider HHH is the sequence of steps of DD
simulated by HHH according to the semantics of
the C programming language.
(2) Turing Machine based Computable functions
only transform input finite strings into some value.
Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument.
https://en.wikipedia.org/wiki/Computable_function
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
*I will add a little humor for levity*
DD() executed from main() that calls HHH(DD)
as one-and-the-same-thing as an argument to HHH.
*Would be like I am my own grandpa*
https://www.streetdirectory.com/lyricadvisor/song/euwflw/im_my_own_grandpa/
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
This required establishing a new foundation
for correct reasoning.
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