On 5/10/2021 10:18 AM, Mike Terry wrote:
> On 10/05/2021 04:25, olcott wrote:
>> **My whole proof is boiled down to as simple as this:**
>> When the execution trace of H_Hat() correctly matches a correct
>> non-halting behavior pattern then the decision of non-halting is
>> impossibly incorrect: AKA modal logic necessarily(P)
>>
>> When an execution trace matches the following criteria we know that
>> the non-halting behavior of infinite recursion or infinitely nested
>> simulation has been matched:
>>
>> If the execution trace of function Y() shows:
>> (1) function X() is called twice in sequence from the same machine
>> address of Y()
>> (2) with the same parameters to X()
>> (3) with no conditional branch or indexed jump instructions in Y()
>> (4) with no function call returns from X()
>> then the function call from Y() to X() is infinitely recursive.
>
> You cut the lines that said you were intellectually incapable of
> producing any kind of proof, because you don't understand what a proof
> actually is.  The above is not a proof of anything.

As I suspected you never provided any rebuttal at all, you merely
dismissed my sound deductive inference entirely out-of-hand on the basis
that it is not in the form of a conventional mathematical proof.

Simulating partial halt decider H correctly decides that P(P) never halts

// Simplified Linz Ĥ (Linz:1990:319)
void P(u32 x)
{ u32 Input_Halts = H(x, x);
if (Input_Halts)
HERE: goto HERE;
}

int main()
{ u32 Input_Halts = H((u32)P, (u32)P);
Output("Input_Halts = ", Input_Halts);
}

_P()
[00000b1a](01) 55 push ebp
[00000b1b](02) 8bec mov ebp,esp
[00000b1d](01) 51 push ecx
[00000b1e](03) 8b4508 mov eax,[ebp+08]
[00000b21](01) 50 push eax // 2nd Param
[00000b22](03) 8b4d08 mov ecx,[ebp+08]
[00000b25](01) 51 push ecx // 1st Param
[00000b26](05) e81ffeffff call 0000094a // call H
[00000b2b](03) 83c408 add esp,+08
[00000b2e](03) 8945fc mov [ebp-04],eax
[00000b31](04) 837dfc00 cmp dword [ebp-04],+00
[00000b35](02) 7402 jz 00000b39
[00000b37](02) ebfe jmp 00000b37
[00000b39](02) 8be5 mov esp,ebp
[00000b3b](01) 5d pop ebp
[00000b3c](01) c3 ret
Size in bytes:(0035) [00000b3c]

_main()
[00000bda](01) 55 push ebp
[00000bdb](02) 8bec mov ebp,esp
[00000bdd](01) 51 push ecx
[00000bde](05) 681a0b0000 push 00000b1a // push address of P
[00000be3](05) 681a0b0000 push 00000b1a // push address of P
[00000be8](05) e85dfdffff call 0000094a // call H
[00000bed](03) 83c408 add esp,+08
[00000bf0](03) 8945fc mov [ebp-04],eax
[00000bf3](03) 8b45fc mov eax,[ebp-04]
[00000bf6](01) 50 push eax
[00000bf7](05) 683b030000 push 0000033b
[00000bfc](05) e869f7ffff call 0000036a
[00000c01](03) 83c408 add esp,+08
[00000c04](02) 33c0 xor eax,eax
[00000c06](02) 8be5 mov esp,ebp
[00000c08](01) 5d pop ebp
[00000c09](01) c3 ret
Size in bytes:(0048) [00000c09]

Columns
(1) Machine address of instruction
(2) Machine address of top of stack
(3) Value of top of stack after instruction executed
(4) Machine language bytes
(5) Assembly language text
===============================
....[00000bda][00101647][00000000](01) 55 push ebp
....[00000bdb][00101647][00000000](02) 8bec mov ebp,esp
....[00000bdd][00101643][00000000](01) 51 push ecx
....[00000bde][0010163f][00000b1a](05) 681a0b0000 push 00000b1a //
push P
....[00000be3][0010163b][00000b1a](05) 681a0b0000 push 00000b1a //
push P
....[00000be8][00101637][00000bed](05) e85dfdffff call 0000094a //
call H
Begin Local Halt Decider Simulation at Machine Address:b1a
....[00000b1a][002116e7][002116eb](01) 55 push ebp
....[00000b1b][002116e7][002116eb](02) 8bec mov ebp,esp
....[00000b1d][002116e3][002016b7](01) 51 push ecx
....[00000b1e][002116e3][002016b7](03) 8b4508 mov eax,[ebp+08]
....[00000b21][002116df][00000b1a](01) 50 push eax //
push P
....[00000b22][002116df][00000b1a](03) 8b4d08 mov ecx,[ebp+08]
....[00000b25][002116db][00000b1a](01) 51 push ecx //
push P
....[00000b26][002116d7][00000b2b](05) e81ffeffff call 0000094a //
call H
....[00000b1a][0025c10f][0025c113](01) 55 push ebp
....[00000b1b][0025c10f][0025c113](02) 8bec mov ebp,esp
....[00000b1d][0025c10b][0024c0df](01) 51 push ecx
....[00000b1e][0025c10b][0024c0df](03) 8b4508 mov eax,[ebp+08]
....[00000b21][0025c107][00000b1a](01) 50 push eax //
push P
....[00000b22][0025c107][00000b1a](03) 8b4d08 mov ecx,[ebp+08]
....[00000b25][0025c103][00000b1a](01) 51 push ecx //
push P
....[00000b26][0025c0ff][00000b2b](05) e81ffeffff call 0000094a //
call H
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

In the above 16 instructions of the simulation of P(P) we can see that
the first 8 instructions of P are repeated. The end of this sequence of
8 instructions is a call to H(P,P). Because H only examines the behavior
of its inputs and ignores its own behavior when H(P,P) is called we only
see the first instruction of P being simulated.

Anyone knowing the x86 language well enough can see that none of these 8
simulated instructions of P have any escape from their infinitely
repeating behavior pattern. When H recognizes this infinitely repeating
pattern it aborts its simulation of P(P) and reports that its input:
(P,P) would never halt on its input.

....[00000bed][00101643][00000000](03) 83c408 add esp,+08
....[00000bf0][00101643][00000000](03) 8945fc mov [ebp-04],eax
....[00000bf3][00101643][00000000](03) 8b45fc mov eax,[ebp-04]
....[00000bf6][0010163f][00000000](01) 50 push eax
....[00000bf7][0010163b][0000033b](05) 683b030000 push 0000033b
---[00000bfc][0010163b][0000033b](05) e869f7ffff call 0000036a
Input_Halts = 0
....[00000c01][00101643][00000000](03) 83c408 add esp,+08
....[00000c04][00101643][00000000](02) 33c0 xor eax,eax
....[00000c06][00101647][00000000](02) 8be5 mov esp,ebp
....[00000c08][0010164b][00100000](01) 5d pop ebp
....[00000c09][0010164f][00000080](01) c3 ret
Number_of_User_Instructions(33)
Number of Instructions Executed(26452)

> If you're going to submit an article for peer review, the reviewer will
> expect there to be a proof of any claims you make.  So perhaps you have
> some kind of proof of the above claims for (1)-(4) somewhere?  (I
> suggested you should do this 6 months ago, but nothing was forthcoming
> apart from your "I'm making it an axiom" nonsense.
>
> Also, if you're claiming to have refuted the Linz/Sipser/similar HP
> proof, they will expect you to say where exactly the error is in those
> proofs.  Saying "my computer program shows they're wrong" won't cut it!
> (But feel free to try that anyway...)
>
>
> Regards,
> Mike.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein