Re: Defining a correct simulating halt decider

On 2024-09-06 11:42:48 +0000, olcott said:
 

On 9/6/2024 6:19 AM, Mikko wrote:

On 2024-09-05 13:24:20 +0000, olcott said:
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On 9/5/2024 2:34 AM, Mikko wrote:

On 2024-09-03 13:00:50 +0000, olcott said:
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On 9/3/2024 5:25 AM, Mikko wrote:

On 2024-09-02 16:38:03 +0000, olcott said:
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A halt decider is a Turing machine that computes
the mapping from its finite string input to the
behavior that this finite string specifies.

>
A halt decider needn't compute the full behaviour, only whether
that behaviour is finite or infinite.
>

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void DDD()
{
   HHH(DDD);
   return;
}
>
New slave_stack at:1038c4
Begin Local Halt Decider Simulation   Execution Trace Stored at:1138cc
[00002172][001138bc][001138c0] 55         push ebp      ; housekeeping
[00002173][001138bc][001138c0] 8bec       mov ebp,esp   ; housekeeping
[00002175][001138b8][00002172] 6872210000 push 00002172 ; push DDD
[0000217a][001138b4][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
New slave_stack at:14e2ec
[00002172][0015e2e4][0015e2e8] 55         push ebp      ; housekeeping
[00002173][0015e2e4][0015e2e8] 8bec       mov ebp,esp   ; housekeeping
[00002175][0015e2e0][00002172] 6872210000 push 00002172 ; push DDD
[0000217a][0015e2dc][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
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Hence  HHH(DDD)==0 is correct

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Nice to see that you don't disagree with what said.
Unvortunately I can't agree with what you say.
HHH terminates,

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os DDD obviously terminates, too. No valid

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DDD emulated by HHH never reaches it final halt state.

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If that iis true it means that HHH called by DDD does not return
and therefore is not a ceicder.
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The directly executed HHH is a decider.

 If the called HHH behaves differently from the direcly executed HHH
then the DDD is not relevant to classic proofs of the impossibility
of a halting decider.
 If you can't show encoding rules that permit the encoidng of the
behaviour of the directly executed DDD to HHH then HHH is not a
halting decider.