Refuting the halting problem proofs

[olcott]

To overcome the pathological self-reference error of the conventional
halting problem proofs we simply define halt decider H such that every
input P to halt decider H that itself calls H has the same halting value
as the halting value as input P2 adapted from input P where all calls to
H have been replaced with calls to Simulate.

We can see that on the basis of this corrected criteria the actual Linz
H would correctly decide not halting on the actual Linz Ĥ shown on page
319. http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf



Does the simulation of input P by simulating (at least partial) halt
decider H have to be stopped to prevent the infinite execution of P?

void H_Hat(u32 P)
{
u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
}

THIS IS A TRUISM:
If the simulation never needs to be stopped then we can swap
Simulate(P,P) for Halts(P,P) and it will stop otherwise we know that the
simulation must have needed to have been stopped at some point.

http://www.liarparadox.org/Halting_problem_undecidability_and_infinitely_nested_simulation.pdf



--
Copyright 2021 Pete Olcott

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

[Bonita Montero]

STOP POSTING in comp.lang.c/c++ !!!

[olcott]

On 5/15/2021 10:57 PM, Bonita Montero wrote:
> STOP POSTING in comp.lang.c/c++ !!!

No

[Bonita Montero]

>> STOP POSTING in comp.lang.c/c++ !!!

> No

You don't post anything related specifically to C or C++,
so stop postingg here.

[olcott]

Everything that I post to is directly related to the correctness of
the following C code: (executed in the x86utm OS written in C and C++)

void H_Hat(u32 P)
{
u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
}

int main()
u32 Input_Would_Halt = Halts((u32)H_Hat, (u32)H_Hat);
Output("Input_Would_Halt = ", Input_Would_Halt);
}

When the behavior of the input Ĥ to simulating halt decider H
(a) correctly matches
(b) a correct non-halting behavior pattern
then H decides non-halting on Ĥ correctly.

Halts returns 0 on the basis that the behavior of H_Hat matches
the [infinitely_nested_simulation] not halting behavior pattern.

If the above C code is correct then this proves that all
the conventional halting problem instances can be decided
as not halting. The following is from Peter Linz:

Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn

H.qx wM wM ⊢* H.qy
H.qx wM wM ⊢* H.qn

H applied to input (Ĥ, Ĥ) transitions to H.qn on the basis that
the behavior of Ĥ matches the [infinitely_nested_simulation]
not halting behavior pattern.

http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf



http://www.liarparadox.org/Halting_problem_undecidability_and_infinitely_nested_simulation.pdf

[Bonita Montero]

> Everything that I post to is directly related to the correctness of
> the following C code: (executed in the x86utm OS written in C and C++)

You're problems are generic for most languages.
You don't write about specific C- or C++-problems.
So please stop posting here.