XPost: comp.theory, sci.logic, sci.math
// Simplified Linz(1990) Ĥ
// and Strachey(1965) P
void P(ptr x)
{
if (H(x, y))
HERE: goto HERE;
}
H and P are defined according to the standard HP counter-example
template shown above.
H bases its halt status decision on the behavior of the simulation of
its input.
Then P demonstrates an infinitely repeating pattern that cannot possibly
ever reach its final state.
This conclusively proves that the input to H meets the Linz definition
of non-halting:
computation that halts … the Turing machine will halt whenever it enters
a final state. (Linz:1990:234)
thus the sufficiency condition for H to report that its input specifies
a non-halting computation.
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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