Halt deciders only compute the mapping from their inputs to an accept or
reject state on the basis of the actual behavior of this input.

The correct simulation of 1 to ∞ steps of a machine description provides
the actual behavior of of 1 to ∞ steps of the underlying machine.

int Hx(ptr x, ptr y);

void Px(ptr x)
{ int Halt_Status = Hx(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}

A simulating halt decider (SHD) continues to simulate its input until
the behavior of this input matches a non-halting behavior pattern or the
simulated input halts on its own.

There are zero Px elements of infinite set of Hx/Px pairs such that the
correct simulation (of 1 to ∞ steps) or direct execution of Px by Hx
reaches the final state of Px and halts.

Some of the Hx elements correctly recognize a correct non-halting
behavior pattern proving that its Px never halts. These Hx elements
correctly abort their simulation and correctly return 0 for non-halting.

*This Hx/Px pair is named H/P and is fully operational*

Complete halt deciding system (Visual Studio Project)
(a) x86utm operating system
(b) complete x86 emulator adapted from libx86emu
(c) Several halt deciders and their inputs contained within Halt7.c
https://liarparadox.org/2022_09_07.zip

The recursive simulation non-halting behavior pattern is slightly
adapted from infinite recursion behavior pattern used to determine the
halt status of void Infinite_Recursion(u32 N).

Once the infinite recursion behavior pattern is understood to be correct
then the recursive simulation behavior pattern is also understood to be
correct. Both of these behavior patterns use the exact same non-halting
criteria.

*Halting problem proofs refuted on the basis of software engineering*
https://www.researchgate.net/publication/361701808_Halting_problem_proofs_refuted_on_the_basis_of_software_engineering

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

On 9/28/2022 3:05 PM, Paul N wrote:
> On Wednesday, September 28, 2022 at 5:43:26 PM UTC+1, olcott wrote:
>> On 9/28/2022 11:32 AM, Mr Flibble wrote:
>>> On Tue, 27 Sep 2022 16:10:01 -0500
>>> olcott <non...@beez-waxes.com> wrote:
>>>
>>>> On 9/27/2022 3:36 PM, Mr Flibble wrote:
>>>>> On Tue, 27 Sep 2022 10:49:02 -0500
>>>>> olcott <polc...@gmail.com> wrote:
>>>>>
>>>>>> Halt deciders only compute the mapping from their inputs to an
>>>>>> accept or reject state on the basis of the actual behavior of this
>>>>>> input.
>>>>>
>>>>> And your decider doesn't do that so it isn't a halt decider, it is a
>>>>> recursive simulation decider. Real halt deciders return a decision
>>>>> to their caller in finite time.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> My code speaks for itself, thus conclusively proves that you don't
>>>> have a clue.
>>>
>>> Your code speaks for itself: it doesn't meet the functional
>>> requirements of a halt decider. You don't have a clue.
>>>
>>> /Flibble
>>>
>> You simply don't have the mental discipline to pay enough attention to
>> understand my rebuttals of your claims.
>>
>> Halt deciders must compute the mapping from their inputs to a final
>> accept or reject state on the basis of the actual behavior specified by
>> these inputs.
>
> Yes. You keep trying to pull a sleight-of-hand by saying that what counts is not the actual behaviour but what a correct simulation would do. This is not actually correct because P cannot be simulated properly. You then say that your simulation is correct, despite it giving the wrong answers. You justify that by claiming that no-one has found a flaw in it, despite several people pointing out the flaws numerous times, which you wave away by claiming, with no proof, that they are all wrong.
>

I HAVE ALREADY BEEN THOUGH THIS HUNDREDS OF TIMES
It is easily verified that the simulation is correct in that the
simulated x86 instructions exactly match what their x86 source-code
specifies.

Furthermore:

void Px(ptr x)
{ int Halt_Status = Hx(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}

int main()
{ Output("Input_Halts = ", Hx(Px, Px));
}

There are zero elements of infinite set of Hx/Px pairs such that the
correct *partial or complete* simulation of Px by Hx reaches the final
state of Px and halts. This is also the case when Hx directly executes Px.

My reviewers simply are not bright enough to see this thus mistakenly
believe that I am wrong.

Complete halt deciding system (Visual Studio Project)
(a) x86utm operating system
(b) complete x86 emulator adapted from libx86emu
(c) Several halt deciders and their inputs contained within Halt7.c
https://liarparadox.org/2022_09_07.zip

--
Copyright 2022 Pete Olcott

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

On 9/29/2022 9:45 AM, Paul N wrote:
> On Thursday, September 29, 2022 at 2:49:07 PM UTC+1, olcott wrote:
>> On 9/28/2022 3:05 PM, Paul N wrote:
>>> On Wednesday, September 28, 2022 at 5:43:26 PM UTC+1, olcott wrote:
>>>> On 9/28/2022 11:32 AM, Mr Flibble wrote:
>>>>> On Tue, 27 Sep 2022 16:10:01 -0500
>>>>> olcott <non...@beez-waxes.com> wrote:
>>>>>
>>>>>> On 9/27/2022 3:36 PM, Mr Flibble wrote:
>>>>>>> On Tue, 27 Sep 2022 10:49:02 -0500
>>>>>>> olcott <polc...@gmail.com> wrote:
>>>>>>>
>>>>>>>> Halt deciders only compute the mapping from their inputs to an
>>>>>>>> accept or reject state on the basis of the actual behavior of this
>>>>>>>> input.
>>>>>>>
>>>>>>> And your decider doesn't do that so it isn't a halt decider, it is a
>>>>>>> recursive simulation decider. Real halt deciders return a decision
>>>>>>> to their caller in finite time.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> My code speaks for itself, thus conclusively proves that you don't
>>>>>> have a clue.
>>>>>
>>>>> Your code speaks for itself: it doesn't meet the functional
>>>>> requirements of a halt decider. You don't have a clue.
>>>>>
>>>>> /Flibble
>>>>>
>>>> You simply don't have the mental discipline to pay enough attention to
>>>> understand my rebuttals of your claims.
>>>>
>>>> Halt deciders must compute the mapping from their inputs to a final
>>>> accept or reject state on the basis of the actual behavior specified by
>>>> these inputs.
>>>
>>> Yes. You keep trying to pull a sleight-of-hand by saying that what counts is not the actual behaviour but what a correct simulation would do. This is not actually correct because P cannot be simulated properly. You then say that your simulation is correct, despite it giving the wrong answers. You justify that by claiming that no-one has found a flaw in it, despite several people pointing out the flaws numerous times, which you wave away by claiming, with no proof, that they are all wrong.
>>>
>> I HAVE ALREADY BEEN THOUGH THIS HUNDREDS OF TIMES
>> It is easily verified that the simulation is correct in that the
>> simulated x86 instructions exactly match what their x86 source-code
>> specifies.
>
> On the contrary, you've told us numerous times that Px halts but Hx "correctly" predicts that it doesn't.

Sure and if I am "told" that squares are round I will take it the same
way. The things that clueless wonders tell me carry no weight.

> That is *not* a correct simulation. You are assuming that Hx is correct in assuming that it has got stuck in a loop, when you know full well that Hx has the machinery to get out of the loop, because you wrote it yourself.
>

H and P are C functions that I wrote. Hx/Px is an infinite set of
different definitions of Hx for the following Px.

>> Furthermore:
>>
>> void Px(ptr x)
>> {
>> int Halt_Status = Hx(x, x);
>> if (Halt_Status)
>> HERE: goto HERE;
>> return;
>> }
>>
>> int main()
>> {
>> Output("Input_Halts = ", Hx(Px, Px));
>> }
>
> Yes, it is clear that Px will do the opposite of what Hx "predicts" it will do.
>
>> There are zero elements of infinite set of Hx/Px pairs such that the
>> correct *partial or complete* simulation of Px by Hx reaches the final
>> state of Px and halts. This is also the case when Hx directly executes Px.
>
> Why do you keep saying this? There are no pairs where Hx correctly simulates Px.

No sense talking to you anymore because you lack the technical
competence to see that H does correctly emulate P using an x86
emulator. You don't even know C well enough to see that when Hx
correctly simulates 1 to ∞ steps of Px that Px never reaches its
own final state.

// H(Px,Px) directly executes Px that never halts.
//
int Hx(ptr x, ptr y)
{ x(y);
}

Since halt deciders only compute the mapping from their inputs
to an accept or reject state based on the actual behavior
specified by these inputs THE BEHAVIOR OF NON INPUTS IS IRRELEVANT
EVEN IF YOUR GROUP-THINK BUDDIES THINK THAT IT IS.

Groupthink is a phenomenon that occurs when a group of well-intentioned
people makes irrational or non-optimal decisions spurred by the urge to
conform or the belief that dissent is impossible. The problematic or
premature consensus that is characteristic of groupthink may be fueled
by a particular agenda—or it may be due to group members valuing harmony
and coherence above critical thought.
https://www.psychologytoday.com/us/basics/groupthink

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer