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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,comp.lang.c,sci.logic,sci.math
Subject: Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT
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Date: Fri, 18 Apr 2025 11:19:23 -0500
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On 4/18/2025 8:27 AM, Mr Flibble wrote:
> On Wed, 16 Apr 2025 23:24:22 +0100, Richard Heathfield wrote:
> 
>> On 16/04/2025 22:01, Mr Flibble wrote:
>>> I, aka Mr Flibble, have uniquely identified this category error and
>>> have thus solved the halting problem
>>
>> No, Mr Flibble, you have solved the Mr Flibble Problem. Well done! You
>> may award yourself whatever cash prize you can find in your piggy bank.
>> Well done!
>>
>> And now you'd hurry back to using all those naughty words while your
>> mummy's still out at the shops.
> 
> Partial deciders are a thing,

Yes they are and termination analyzers only need
be correct on at least one input.

>  dear, and in the case of a simulating halt
> decider with finite resources repeated state can be recognised for a
> useful subset of problems including the ability to recognise pathological
> input (halting problem category error manifestation). A simulating halt

Yes.
> decider with the mythical infinite resources that the halt decider that
> your proofs are predicated on also possesses is an unpartial decider also
> with the ability to recognise pathological input (halting problem category
> error manifestation).
> 
> /Flibble

typedef void (*ptr)();
int HHH(ptr P);

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

int main()
{
   HHH(DD);
} SIMULATED DD


It is correct for HHH to reject its input DD as
non-terminating on the basis that DD SIMULATED BY
HHH and HHH emulating itself emulating DD prove a
repeating pattern preventing the

// dishonest people tried to change this subject for three years
// dishonest people tried to change this subject for three years
// dishonest people tried to change this subject for three years
SIMULATED DD
SIMULATED DD
SIMULATED DD
SIMULATED DD
SIMULATED DD

 From ever reaching its own final halt state.
The above refutes the conventional Halting Problem proof.
The simulating halt decider / termination analyzer is my idea.

Flibble's signalling halt decider is also very useful
because it looks at both of two options.

Computer Science professor Eric Hehner independently derived
the prequel to a simulating halt decider (see quote below)
[5] E C R Hehner. Problems with the Halting Problem, COMPUTING2011 
Symposium on 75 years of Turing Machine and Lambda-Calculus, Karlsruhe 
Germany, invited, 2011 October 20-21; Advances in Computer Science and 
Engineering v.10 n.1 p.31-60, 2013

*Professor Hehner recognized this repeating process before I did*
   From a programmer's point of view, if we apply an
   interpreter to a program text that includes a call
   to that same interpreter with that same text as
   argument, then we have an infinite loop. A halting
   program has some of the same character as an interpreter:
   it applies to texts through abstract interpretation.
   Unsurprisingly, if we apply a halting program to a program
   text that includes a call to that same halting program with
   that same text as argument, then we have an infinite loop.
   (Hehner:2011:15) https://www.cs.toronto.edu/~hehner/PHP.pdf


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer