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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Defining a correct simulating halt decider
Date: Sat, 7 Sep 2024 11:27:52 +0300
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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:
>>
>>> On 9/5/2024 2:34 AM, Mikko wrote:
>>>> On 2024-09-03 13:00:50 +0000, olcott said:
>>>>
>>>>> On 9/3/2024 5:25 AM, Mikko wrote:
>>>>>> On 2024-09-02 16:38:03 +0000, olcott said:
>>>>>>
>>>>>>> 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.
>>>>>>
>>>>>
>>>>> 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
>>>>>
>>>>> Hence HHH(DDD)==0 is correct
>>>>
>>>> Nice to see that you don't disagree with what said.
>>>> Unvortunately I can't agree with what you say.
>>>> HHH terminates,
>>>
>>>> os DDD obviously terminates, too. No valid
>>>
>>> DDD emulated by HHH never reaches it final halt state.
>>
>> If that iis true it means that HHH called by DDD does not return
>> and therefore is not a ceicder.
>>
>
> 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.
--
Mikko