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Validating that H correctly determines the halt status of D

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olcott

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Nov 13, 2022, 11:56:09 PM11/13/22
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Every rebuttal of my work in the last two years only has rejecting the
notion of a simulating halt decider as its basis.

Once a simulating halt decider is accepted then ordinary software
engineering proves that H correctly determines the halt status of D.

MIT Professor Michael Sipser (author of the best selling book on the
theory of computation) has agreed that the following verbatim paragraph
is correct (he has not agreed to anything else):

If simulating halt decider H correctly simulates its input
D until H correctly determines that its simulated D would
never stop running unless aborted then H can abort its
simulation of D and correctly report that D specifies a
non-halting sequence of configurations.

void D(void (*x)())
{
int Halt_Status = H(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}

int main()
{
Output("Input_Halts = ", H(D, D));
}

(A) The definition of a UTM proves that the behavior of a correctly
simulated input is a correct halt deciding basis for a simulating halt
decider.

(B) The line-by-line execution trace of D simulated by H exactly matches
what the line-by-line x86 source code of D specifies conclusively proves
that the simulation of D by H is correct.

(C) D correctly simulated by H would never reach its final state and
terminate normally.

(X) A&B&C form the necessary and sufficient conditions for H to reject D
as non-halting.

*My reviewers don't seem to be able to grasp this essential detail*
When A&B&C entails X and A&B&C then X is entailed no matter what or who
disagrees. My reviewers know this this logic is correct yet have failed
to notice that A&B&C entails X.

*A&B&C also meets the Sipser approved criteria*
H correctly simulates its input D until H correctly determines
that its simulated D would never stop running unless aborted.

*Simulating Halt Decider Applied to the Halting Theorem*
https://www.researchgate.net/publication/364657019_Simulating_Halt_Decider_Applied_to_the_Halting_Theorem

--
Copyright 2022 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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