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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: Sun, 12 May 2024 12:58:16 -0400
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On 5/12/24 9:59 AM, olcott wrote:
> On 5/12/2024 3:45 AM, Mikko wrote:
>> On 2024-05-11 16:35:48 +0000, olcott said:
>>
>>> On 5/11/2024 4:39 AM, Mikko wrote:
>>>> On 2024-05-11 00:30:40 +0000, olcott said:
>>>>
>>>>> A termination analyzer is different than a halt decider in that it 
>>>>> need
>>>>> not correctly determine the halt status of every input. For the 
>>>>> purposes
>>>>> of this paper a termination analyzer only needs to correctly determine
>>>>> the halt status of one terminating input and one non-terminating 
>>>>> input.
>>>>> The computer science equivalent would be a halt decider with a limited
>>>>> domain that includes at least one halting and one non-halting input.
>>>>
>>>> From https://www.google.fi/search?q=termination+analysis and
>>>> https://en.wikipedia.org/wiki/Termination_analysis :
>>>>
>>>> "In computer science, termination analysis is program analysis which 
>>>> attempts to determine whether the evaluation of a given program 
>>>> halts for each input. This means to determine whether the input 
>>>> program computes a total function."
>>>>
>>>> So the term "termination analysis" is already defined. The derived term
>>>> "termination analyzer" means a performer of termination analysis. That
>>>> does not agree with the propsed defintion above so a differnt term
>>>> should be used.
>>>>
>>>> That "termination analysis" is a know term that need not be defined
>>>> is demostrated e.g. by
>>>>
>>>>    https://arxiv.org/pdf/2101.09783
>>>>
>>>> which simply assumes that readers know (at least approximately) what
>>>> the term means.
>>>>
>>>
>>> You are doing a great job performing an honest review!
>>> So every time that Richard referred to a {termination analyzer} that
>>> ignores its inputs *Richard was WRONG*
>>
>> More important is that you are wrong whenever you use "termination
>> analyser" for something that by the conventional meaning isn't.
>>
> 
> A conventional termination analyzer is free to use any algorithm
> as long as it analyzes termination.

Including not simulating any steps.


> 
>> In particular, one thing that needs be considered is the input space.
>> A particular input is not relevant.
>>
> 
> A particular input is 100% relevant when trying to determine
> the halt status of this input.
> 
> *The pathology of an input CANNOT BE IGNORED*

Right, and thus H can't ignore that D calls THE DEFINED H, which you 
claim returns 0, and thus doesn't run forever.

> 
> When Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> It <is> the case that the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ never stops running
> unless aborted when embedded_H is a simulating termination analyzer.
> 

But since embedded_H WILL abort its simulation, (or H never answers and 
fails to be a decider), this logic is based on a false premise.


> People can lie about this. What they cannot do is show steps proving
> that it does stop running without being aborted.
> 

It HAS been shown that the CORRECT simulation of the input to H(D,D) 
will terminate without being aborted. The key is that you H doesn't do a 
correct simulation.


Yes, your template creates a set of programs, that none of the limited 
set of simulating "Halt Deciders" will be able to simulate there input 
to a final state.

The problem is that this is NOT the definition of Halting or Non-Halting 
or what a Halt Decider is supposed to decide on.

You are just working on your POOP.