Re: The philosophy of computation reformulates existing ideas on a new basis

On 2024-11-07 16:39:57 +0000, olcott said:

On 11/7/2024 3:56 AM, Mikko wrote:

On 2024-11-06 15:26:06 +0000, olcott said:
 

On 11/6/2024 8:39 AM, Mikko wrote:

On 2024-11-05 13:18:43 +0000, olcott said:
 

On 11/5/2024 3:01 AM, Mikko wrote:

On 2024-11-03 15:13:56 +0000, olcott said:
 

On 11/3/2024 7:04 AM, Mikko wrote:

On 2024-11-02 12:24:29 +0000, olcott said:
 

HHH does compute the mapping from its input DDD
to the actual behavior that DDD specifies and this
DOES INCLUDE HHH emulating itself emulating DDD.

 Yes but not the particular mapping required by the halting problem.

 Yes it is the particular mapping required by the halting problem.
The exact same process occurs in the Linz proof.

 The halting probelm requires that every halt decider terminates.
If HHH(DDD) terminates so does DDD. The halting problmen requires
that if DDD terminates then HHH(DDD) accepts as halting.

 void Infinite_Loop()
{
   HERE: goto HERE;
   return;
}
 No that is false.
The measure is whether a C function can possibly
reach its "return" instruction final state.

 Not in the original problem but the question whether a particular strictly
C function will ever reach its return instruction is equally hard. About

 It has always been about whether or not a finite string input
specifies a computation that reaches its final state.

 Not really. The original problem was not a halting problem but Turing's

 Exactly. The actual Halting Problem was called that by Davis
in 1952. Not the same as Turing proof.

In early times there was variation in how things were presented and what
words were used. Post had studied the halting problem of his tag system
much earlier but didn't call it a machine. Many other problems were also
studied and later found to be more or less related to the halting
problem and its variants.

*So we are back to The Halting Problem itself*
 has always been about whether or not a finite string input
specifies a computation that reaches its final state.

No, it has been a collection of related problems that includes that
particular one. As the problems are related and equally hard it does
not really matter which one you choose as long as you are clear
about your choice. To argue about the meaning of words id a clear
indcation of an intent to avoid an honest discussion.
--
Mikko