On 10/15/2025 3:47 PM, Kaz Kylheku wrote:I didn't get the correct understanding by beingOn 2025-10-15, olcott <polcott333@gmail.com> wrote:Great I just tested this and ChatGPT 5.0 and Gemini getPlease think this all the way through without making any guesses.>
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Simulating Termination Analyzer HHH correctly simulates its input until:
This sentence must end with nothing other than "until that input terminates".
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Otherwise the simulation is not complete and correct.
>(a) Detects a non-terminating behavior pattern:>
abort simulation and return 0.
(b) Simulated input reaches its simulated "return" statement:
return 1.
(c) If HHH must abort its simulation to prevent its own non-termination
then HHH is correct to abort this simulation and return 0.
HHH is correct to abort the simulation because if it doesn't do that,
it will not terminate. All halting deciders that incorporate simulation
as a tool must break out of simulation at some point in order not to be
tripped up by inputs that fail to terminate.
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the wrong answer without (c). ChatGPT 4.0, Claude AI
and Grok all got this same answer without (c) and
without being told not to guess.
Without breaking out of the simulation, it would not be possibleYes.
for HHH(Infinite_Loop) or HHH(Infinite_Recursion) to decide correctly
that the return value should be zero.
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However, nothing is effective against the diagonal input.Unless we go be the behavior that the semantics
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of the specification language specifies as the
ultimate judge.
Not within the stipulated axioms when (c) is invoked.What value should HHH(DD) correctly return?>
The set of possible solutions is the empty set.Its deeper than that. See my other post.
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3x + y = 5
6x + 2y = 3
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What pairs <x, y> satisfy these equations?
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HHH(DD) not having a solution is no different from simultaneous
equations in n variables not having a solution.
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Elementary school children can work with these.
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a brilliant computer scientist. I got it by focusing
on how pathological self-reference effects truth.
I did this with an OCD like focus of concentration
for 28 years.
In the top of my new post [The Halting Problem is Incoherent]
I show exactly how to overcome Quine's objection to the
analytic / synthetic distinction. This is a key aspect of the
foundation of the notion of truth itself.
--
Copyright 2025 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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