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

On 2024-11-09 14:56:14 +0000, olcott said:

On 11/9/2024 3:53 AM, Mikko wrote:

On 2024-11-08 14:39:20 +0000, olcott said:
 

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

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.

 The halting problem has always been abuut halting

 Nevertheless Turing's solution to his circularity problem is usually
regarded as the first solution to the halting problem.
 

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.

 

It is not the meaning of words it is the semantic
property of the finite string pair HHH/DDD.

 Above you have argued about the meanings of the words and
keep doing so below.

 It is the meaning of the bytes of x86 code and
bytes of code are not words.

No, nothing you have said tells anuything about meanings of the bytes
of x86 code. (A pair of such bytes is sometimes called a "word").
You were just arguing about the meanings the verb "halt" and other
words.

The halting problem has always been about whether a finite
string input specifies a computation that will reach its
final halt state.
 If you disagree then you must provide a complete and coherent
counter-example conclusively proving otherwise not merely
some vague reference to some other things somewhere else.

 From https://www.tutorialspoint.com/automata_theory/ turing_machine_halting_problem.htm
 

Turing Machine Halting Problem
Input − A Turing machine and an input string w.
Problem − Does the Turing machine finish computing of the string w in a finite number of steps? The answer must be either yes or no.

 The computation specified by the finite string DDD
emulated by HHH cannot possibly reach its "return"
instruction final halt state.

It can and does if HHH is a decider and otherwise does not matter.

The computation specified by the finite string DDD
emulated by HHH1 IS NOT THE ACTUAL INPUT TO HHH.

HHH1 can take same inputs as HHH. These inputs specify some behaviour.
What they do with this input may differ.

HHH must compute the mapping FROM ITS INPUT TO THE
BEHAVIOR THAT THIS INPUT SPECIFIES.

Not to full behaviour but to one feature of that behaviour.
Doesn't HHH1 need to?
--
Mikko