XPost: comp.theory, sci.logic, sci.math

On 10/1/2021 11:12 AM, wij wrote:

On Wednesday, 29 September 2021 at 11:20:35 UTC+8, olcott wrote:

The halting theorem counter-examples present infinitely nested
simulation (non-halting) behavior to every simulating halt decider.

-----1-----------2--3----------
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞

If the simulation of the 2nd ⟨Ĥ⟩ applied to
the 3rd ⟨Ĥ⟩ at Ĥ.qx reaches its final state.


-----1-----------2--3----------
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

If the simulation of the 2nd ⟨Ĥ⟩ applied to
the 3rd ⟨Ĥ⟩ at Ĥ.qx never reaches its final state.


https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation

Apparently, you are trying to solve an undecidable problem:
GUR https://groups.google.com/g/comp.theory/c/_tbCYyMox9M

Your proof is essentially several lines of "C" program, nothing to do with
TM or the traditional Halting Problem.

The key basis of your refutation is a refutation to your own conception that no one care. You were denying some part of yourself, not the HP.

I find the key essence is that your relevant knowledge is very weak, you read text books but not doing exercises.
Do exercises in the text books of C,Assembly or Computation theory you read. That would take much lesser time than 7 years (rumor sayed that you have been working on that several lines of C codes for probably more than 7 years!).

It may superficially seem that way.
This is the essence of the basis of my refutation:

The halting theorem counter-examples present infinitely nested
simulation (non-halting) behavior to every simulating halt decider.

I created the x86utm operating system so that every single detail of
theory of computation problems can be analyzed at the much higher level
of abstraction of the C/x86 languages. Without this much higher level abstraction key elements of the HP proof are essentially validated by hand-waving.

https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation


A key element that had taken me by complete surprise is that some things
that are C/x86 computable are not TM computable. I had previously
thought that the Church-Turing thesis confirmed that any and all things
that any physically existing computer can do a TM can compute.



https://en.wikipedia.org/wiki/Computable_function#Characteristics_of_computable_functions

It seems that no aspect of the definition of [computable function]
requires it to be a [pure function], none-the-less most expert opinion
seems to indicate that this requirement exists. I am on the verge of reproducing my work such that the simulating partial halt deciders H1
and H are pure functions and take finite string parameters. To conform
my C/x86 code to the Linz Ĥ template P will copy its input.


In computer programming, a pure function is a function that has the
following properties:

(1) The function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable
reference arguments or input streams).

(2) The function application has no side effects (no mutation of local
static variables, non-local variables, mutable reference arguments or input/output streams).

https://en.wikipedia.org/wiki/Pure_function

--
Copyright 2021 Pete Olcott

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

--
Copyright 2021 Pete Olcott

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

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