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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Termination analyzer defined ---RICHARD IS WRONG !!!
Date: Thu, 16 May 2024 13:02:35 +0300
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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.

-- 
Mikko