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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Termination analyzer defined ---OLCOTT IS WRONG !!!
Date: Thu, 16 May 2024 22:29:29 -0400
Organization: i2pn2 (i2pn.org)
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On 5/16/24 10:21 AM, olcott wrote:
> On 5/16/2024 5:02 AM, Mikko wrote:
>> On 2024-05-15 14:55:26 +0000, olcott said:
>>
>>> On 5/15/2024 2:56 AM, Mikko wrote:
>>>> On 2024-05-14 14:18:40 +0000, olcott said:
>>>>
>>>>> On 5/14/2024 4:34 AM, Mikko wrote:
>>>>>> On 2024-05-13 18:07:37 +0000, Jeff Barnett said:
>>>>>>
>>>>>>> On 5/13/2024 3:06 AM, Mikko wrote:
>>>>>>>
>>>>>>>> Anyway, if an analyzer can never tell whether a program terminates
>>>>>>>> with every possible input then it is not a termination analyzer.
>>>>>>>
>>>>>>> I don't think the above is true in the way you meant it. Recall 
>>>>>>> that the collection of all Turing machines with blank input tapes 
>>>>>>> is the same set of computations as the collection with arbitrary 
>>>>>>> input tapes. It's always possible to take any specific machine, 
>>>>>>> T, and initial tape, I, and produce machine T' with blank initial 
>>>>>>> input tape that is equivalent: T' initially writes I on its tape 
>>>>>>> (say one character output per state in sequence) then continues 
>>>>>>> with the set of states that comprises T.
>>>>>>>
>>>>>>> So it is obvious that a termination analyzer (AKA a halt decider) 
>>>>>>> restricted to blank tape problems will do quite nicely and it is 
>>>>>>> also quite obvious that no such entity exists.
>>>>>>
>>>>>> You only discuss halting decisions with specific inputs. THerefore 
>>>>>> you say
>>>>>> nothing about termination analyzers and don't show any mistake in 
>>>>>> my comment.
>>>>>>
>>>>>
>>>>> 00 int H(ptr x, ptr x)  // ptr is pointer to int function
>>>>> 01 int D(ptr x)
>>>>> 02 {
>>>>> 03   int Halt_Status = H(x, x);
>>>>> 04   if (Halt_Status)
>>>>> 05     HERE: goto HERE;
>>>>> 06   return Halt_Status;
>>>>> 07 }
>>>>> 08
>>>>> 09 int main()
>>>>> 10 {
>>>>> 11   H(D,D);
>>>>> 12 }
>>>>>
>>>>> In any case you diverged away form the whole point of this thread.
>>>>> Richard is wrong when he says that there exists an H/D pair such
>>>>> that D simulated by H ever reaches past its own line 03.
>>>>
>>>> The main topic (per OP) is the definition of "termination analyzer".
>>>> Whether someone is wrong about aomeone else is a secondary topic if
>>>> a topic at all, and pretty poitless anyway.
>>>>
>>>
>>> One can analyze whether a specific program will halt with a specific
>>> input.
>>
>> True but irrelevant. A termination analyser analyses a program without
>> any knowledge about specific inputs.
>>
> 
> *If the halting problem is refuted by this then IT IS NOT IRRELEVANT*
> 

But the halting problem isn't refuted by this, as you have admitted you 
are not working on the hatling problem, but on your POOP, because you 
admit to changing the defintions.

> We are merely haggling over what to call it, not that the idea is
> of no value. H is a termination analyzer that correctly analyzes whether
> or not a certain set of C function/input pairs will halt. Here are two
> examples:
> 
> void Infinite_Recursion(u32 N)
> {
>    Infinite_Recursion(N);
> }
> 
> int factorial(int n)
> {
>    if (n >= 1)
>      return n*factorial(n-1);
>    else
>      return 1;
> }
> 
> 
>