Re: DDD specifies recursive emulation to HHH and halting to HHH1

On 3/27/25 1:50 PM, olcott wrote:

On 3/27/2025 2:18 AM, Fred. Zwarts wrote:

Op 27.mrt.2025 om 04:09 schreef olcott:

On 3/26/2025 8:22 PM, Richard Damon wrote:
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_DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov  ebp,esp  ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add  esp,+04
[00002182] 5d         pop  ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
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Non-Halting is that the machine won't reach its final staste even if an unbounded number of steps are emulated. Since HHH doesn't do that, it isn't showing non-halting.
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DDD emulated by any HHH will never reach its final state
in an unbounded number of steps.
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DDD emulated by HHH1 reaches its final state in a finite
number of steps.
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It is not very interesting to know whether a simulator reports that it is unable to reach the end of the simulation of a program that halts in direct execution.

 That IS NOT what HHH is reporting.
HHH correctly rejects DDD because DDD correctly
emulated by HHH cannot possibly reach its own
final halt state.

Then HHH isn't a Halt Decider, as a Halt Decider is supposed to report on if the direct execution of the program.
Since you HHH doesn't actualy DO a correct emulation (since it only does a partial emulation your criteria is just invalid as it is self-contradictory.

 

It is interesting to know:
'Is there an algorithm that can determine for all possible inputs whether the input specifies a program that (according to the semantics of the machine language) halts when directly executed?'

 It is the halts while directly executed that is impossible
for all inputs. No TM can ever report on the behavior of
the direct execution of any other TM.

Sure it can, at least for many cases.

 A TM can only report on the behavior that the machine code
of another TM specifies. When it specifies a pathological
relationship then the behavior caused by the pathological
relationship MUST BE REPORTED.

Right, and that behavior is what the direct execution of that machine code says.
I guess you just don't understand how computers works.
And the behavior of the relationship DOES need to be reported, but HHH can't.
As the pathological behaivor is that
for DDD, since it doesn't test the result but just returns, DDD will always halt if HHH returns ANY answer (and thus isn't truely pathological, and HHH that returns 1 would be correct)
for DD, since it does test the results and act contrary, DD will halt if HHH(DD) says it doesn't, and not halt if HHH(DD) says it does.
The job of the correct decider is to report on that ACTUAL behavior, but since the pathological program can know the answer it will give, it just can't do that. But the correct answer exists for EVERY HHH you care to define, it just isn't what that HHH answers.

 

This question seems undecidable for Olcott.
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