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

#include <stdint.h>
typedef void (*ptr)();

int H(ptr x, ptr y)
{
x(y);
return 1;
}

// Simplified Linz(1990) Ĥ
// and Strachey(1965) P
void P(ptr x)
{
if (H(x, x))
HERE: goto HERE;
}

int main(void)
{
P(P);
}

A simulating halt decider acts as a pure simulator of its input until
after its input halts on its own or the behavior of this input
conclusively proves that it will never halt on its own.

For inputs that never halt on their own H does not return to its caller
until after H has correctly matched non-halting behavior patterns such
as infinite loop or infinite recursion.

This makes it impossible for a pathological input to thwart a correct
halt status decision.

The pathological feedback loop between the halt decider and its input
that otherwise makes inputs like the above impossible for H(P,P) to
decide has been eliminated.

Halt decider theorem Olcott 2021
When-so-ever simulating halt decider H(X,Y) determines that the behavior
of a pure simulation of its input correctly matches a infinite behavior
pattern such that this input never stops running unless its simulation
is aborted: H correctly aborts this input and returns 0.

H is a computable function that accepts or rejects inputs in its domain
on the basis that the pure simulation of these inputs specify a sequence
of configurations stop running without being aborted.


Halting problem undecidability and infinitely nested simulation V2

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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