Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V52 (HP refutation)

[olcott]

On 9/3/2020 3:28 PM, olcott wrote:
> On 9/3/2020 2:23 PM, Kent Dickey wrote:
>> In article <LfmdnRXy2Lp9nMzC...@giganews.com>,
>> olcott  <No...@NoWhere.com> wrote:
>>
>> I'm going to summarize this, as far as I can tell.
>>
>> A proof of the impossibility of constructing a Turing Mahcine which can
>> determine if all possible Turing Machines complete is at:
>> http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf  Theorem
>> 12.1.
>> It's well written and easy to read even if you know little about Turing
>> Machine, and you don't even need to follow the equations to get the idea.
>>
>> It works by assuming H is the Turing Machine (TM) which can determine
>> if any
>> other TM halts.  It then constructs an H' by adding two states that
>> infinitely loop between each other, and H_Hat by copying the input
>> string.
>> It shows that running H_Hat on itself (basically) leads to
>> contradictions.  Therefore H cannot exist.
>>
>> I believe olcott believes that if he constucts a Turing Machine which can
>> detect if some programs halt (call this Turing Machine H2); and then he
>> modifies H2 to form H2' and H2_Hat (by adding the extra states that H'
>> and
>> H_Hat had above) then the contradiction doesn't apply.  And that this
>> would
>> then show the original proof was wrong.
>>
>
> To convey the gist of what I have accomplished with sufficient accuracy:
> I found a way to create the Linz H_Hat such that it correctly decides
> halting on itself.
>
> My H_hat is not precisely the Linz H_Hat because it was not actually
> constructed from an actual universal halt decider.
>
> My H_Hat is not an actual H_Hat because my H_Hat is not a pencil and
> paper machine that hypothetically has unlimited memory.
>
> My H_Hat is computationally equivalent to a Turing machine on equivalent
> input, deriving equivalent output and having the same halting behavior.
>
> My H_Hat correctly decides halting for many variations of itself and
> many other programs that are not variations of H_Hat.
>

My H_Hat equivalent is implemented as a UTM equivalent such that H_Hat
executes itself (or any other UTM or TM equivalent) in Debug-step mode.

It is the Debug_Step(master_state, slave_state) virtual machine
instruction that converts any TM equivalent into a UTM equivalent.
The master UTM equivalent can examine the state of the slave UTM
equivalent after every Debug_Step() is executed.

The x86 language (plus four virtual machine instructions) comprised the
entire UTM equivalent description language.

// allocates memory from Heap_Space.
[A] u32* Allocate(u32 size);

// executes a slave UTM in single step debug mode
[B] u32 Debug_Step(u32* master_state, u32* slave_state);

// Saves the execution state of a UTM to state_data
[C] u32 Save_State(u32* state_data);

// Loads the execution state of a UTM from state_data
[D] u32 Load_State(u32* state_data);

My x86 based UTM equivalent can directly execute the COFF object files
generated by the Microsoft "C" compilers. This lets me write my H_Hat
equivalent in "C".

--
Copyright 2020 Pete Olcott