On 6/3/2021 9:24 AM, olcott wrote:
> *Halting problem undecidability and infinitely nested simulation*
>
> When halting is defined as any computation that halts without ever
> having its simulation aborted then it can be understood that partial
> halt decider H correctly decides not halting on the simplified version
> of the Linz Ĥ.
>
> When this simplified concrete example is fully understood then the exact
> same reasoning can be applied to the actual Linz H correctly deciding
> not halting on its input.
>
> The x86utm operating system was created so that the halting problem
> could be examined concretely in the high level language of C. x86utm UTM
> tape elements are 32-bit unsigned integers. H examines the behavior of
> the x86 emulation of its input. As soon as a non-halting behavior
> pattern is matched H aborts the simulation of its input and decides not
> halting.
>
> int Simulate(u32 P, u32 I)
> {
> ((void(*)(u32))P)(I);
> return 1;
> }
>
> // Simplified Linz Ĥ (Linz:1990:319)
> void H_Hat(u32 P)
> {
> u32 Input_Halts = H(P, P); // Linz H as a partial halt decider
> if (Input_Halts)
> HERE: goto HERE;
> }
>
> int main()
> {
> H((u32)H_Hat, (u32)H_Hat);
> }
>
> A simulating halt decider that never stops simulating its input is
> simply a simulator on this input. If H() never stopped simulating
> H_Hat() then the halting behavior of H_Hat() would be the same as if
> H_Hat() was called by Simulate() instead of H() and invoked Simulate()
> instead of H(), thus never terminating.
>
> Any computation that must have its simulation aborted to prevent its
> otherwise infinite execution is correctly rejected as non-halting.
> Therefore halting is defined as any computation that halts without ever
> having its simulation aborted.
>
> *Linz, Peter 1990*. An Introduction to Formal Languages and Automata.
> Lexington/Toronto: D. C. Heath and Company.
>
> *Halting problem undecidability and infinitely nested simulation (one
> more page than above)*
> https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation
>
> --
>
> 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