Re: Defining a correct simulating halt decider

Op 06.sep.2024 om 13:42 schreef olcott:

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

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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.
 _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]
 Show the details of how DDD emulated by HHH
reaches its own machine address 0000217f.
 00002172, 00002173, 00002175, 0000217a calls HHH(DDD)
then
00002172, 00002173, 00002175, 0000217a calls HHH(DDD)...
 WHAT SHOULD THE NEXT STEPS BE?
 

In a correct simulation (such as by HHH1 and the world class simulator) the call to HHH will process HHH, which returns to DDD and the next instructions in DDD are 0000217f, 00002182, 00002183, after which DDD halts.
But HHH fails to reach this part of the simulation, because it has an error in the algorithm to detect the 'special condition'.
Olcott is still dreaming of a simulated HHH that will not see this 'special condition'. He does not realise that by adding the code to recognize this 'special condition' and stop the simulation, the other HHH, that does not see this 'special condition', disappeared and remains only in his dreams. HHH, when simulating *itself* should now decide about the DDD that uses this new HHH that sees this 'special condition' and aborts.
*That code* is where the problem is, not the incomplete simulation itself.
In fact, if Olcott would have found a solution for the halting problem, then it would not be in the simulation, but in the detection of the 'special condition'. The correctness of the simulation is only relevant because it is used as input for the code to detect the 'special condition'. The proof that the halting problem cannot be solved with a computation implies that Olcott's detection of the 'special condition' cannot be correct.
It is probable that Olcott understands that it cannot be correct and therefore he hides the code for the recognition of this 'special condition'.
He probably knows that if he would publish this part of the decider, people would spot many errors in it immediately.
He has only shown some trivial examples as evidence that this detection of the 'special condition' is correct, such as Infinite_Loop and Infinite_Recursion, but, of course, a few trivial examples do not prove the correctness of this algorithm.
Therefore, he keeps pulling the attention away from the correctness of the detection of the 'special condition', to the correctness of the simulation.