Re: DDD correctly emulated by HHH is Correctly rejected as non-halting V2

On 2024-07-15 13:39:07 +0000, olcott said:

On 7/15/2024 3:09 AM, Mikko wrote:

On 2024-07-14 14:00:55 +0000, olcott said:
 

According to the theory of computation the DDD that calls
HHH(DDD) is not in the domain of HHH.

 The theory of computation does not say what the domain of HHH is.

 Sure it does. Where the Hell have you been?
It says that the halting problem is defined in terms
of finite strings that encode Turing machines.

No, it does not. The halting problem is not a part of any theory of
computation. It is a question that one maight expect the theory of
computation to answer.
Note that the halting problem does not specify how Turing machines
should be encoded to finite strings. It meresly requires that the
solution includes encoding rules so that every Turing machine can be
encoded.

Unless the specificaiton of HHH says otherwise HHH should be able
to handle every input that can be given to it,

 No halt decider is allowed to report on the computation
that it is contained within for several different reasons
one of them is that computations are not finite strings.

The halting problem requires that every Turing machine computation
can be given as input.
A partial halt decider may fail to answer for some computations.
--
Mikko