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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: What is the best way for termination analyzers to handle
 pathological inputs?
Date: Thu, 12 Jun 2025 18:36:10 -0400
Organization: i2pn2 (i2pn.org)
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On 6/12/25 4:13 PM, Mr Flibble wrote:
> On Wed, 11 Jun 2025 18:21:37 -0400, Richard Damon wrote:
> 
>> On 6/11/25 2:21 PM, Mr Flibble wrote:
>>> On Tue, 10 Jun 2025 23:15:51 -0400, Richard Damon wrote:
>>>
>>>> On 6/10/25 3:05 PM, Mr Flibble wrote:
>>>>> On Tue, 10 Jun 2025 14:53:47 -0400, Richard Damon wrote:
>>>>>
>>>>>> On 6/10/25 1:22 PM, olcott wrote:
>>>>>>> On 6/10/2025 2:33 AM, Mikko wrote:
>>>>>>>> On 2025-06-09 21:14:58 +0000, olcott said:
>>>>>>>>
>>>>>>>>> The official "received view" of this is that the best we can
>>>>>>>>> possibly do is to do nothing and give up.
>>>>>>>>
>>>>>>>> There is no official view about "the best". What is the best
>>>>>>>> depends on what one needs and wants. Some may think that the best
>>>>>>>> they can do is to waste their life in trying to do the impossible.
>>>>>>>>
>>>>>>>>
>>>>>>> It is not at all impossible to create a termination analyzer that
>>>>>>> reports on the behavior specified by the input to HHH(DDD). It was
>>>>>>> never correct to define a termination analyzer any other way.
>>>>>>>
>>>>>>>
>>>>>> Right, it is just a fact that it is impossible for HHH to be shuch a
>>>>>> analyzer.
>>>>>>
>>>>>> A CORRECT Temrination analyzer of the input to HHH(DDD), that is to
>>>>>> the termination analysis of DDD, is to say it halts, since the
>>>>>> HHH(DDD) that DDD will call  will return non-halting to that DDD,
>>>>>> and it will then halt.
>>>>>
>>>>> But it will never "return" because it is infinitely recursive; the
>>>>> simulation is aborted and a halting result if non-halting is returned
>>>>> elsewhere.
>>>>>
>>>>> /Flibble
>>>>
>>>> So, you have a problem, either you don't have a correct simulation to
>>>> show you got the right answer, or you don't answer.
>>>>
>>>> That is the problem with trying to have the decider itself be two
>>>> contradictory entities.
>>>>
>>>> A correct simulator can not be a correct decider it the input is
>>>> actually non-halting.
>>>>
>>>> There seems to be some mental block about the fact that the DEFINITION
>>>> of this sort of decider is that:
>>>>
>>>>
>>>> H(M) returns 1 if UTM(M) halts, and H(M) returns 0 if UTM(M) will
>>>> never halt
>>>>
>>>> If you try to combine the the UTM and H into one program that it can
>>>> NEVER correctly return 0, as it can only return 0 if it never halt
>>>> (and thus can't return a value)
>>>
>>> You are wrong. An SHD does not have to simulate an algorithm to
>>> completion if it determines non-halting early BY ANALYSIS.
>>>
>>> /Flibble
>>
>>
>> I didn't say it needed to. But it needs to determine what such a
>> simulation will do.
>>
>> In fact, as I said, if the input IS non-halting, it can't be both the
>> required simulator and the decider, so it is logically inconsistent to
>> say that it is the simulation by the decider that defines the result.
>>
>>
>> t seems you have fallen for Olcott's insanity.
> 
> Here is an analysis of the exchange between **Mr Flibble** and **Richard
> Damon**, with context surrounding the **Simulating Halt Decider (SHD)**
> concept and the **Halting Problem**:

So, you are still appealing to Artifical Intelegence to try to overcome 
your natural stupidity.

The ultimate issue is that to be CORRECT, the answer from the SHD must 
BE correct, and the definition of correct here is well established.

The problem with your "logic" is that you need to rely on categories 
that you can not actually define in an objective manner that lets an 
objective classifier exist.

Without that, a dividing line doesn't exist, and thus no theory can be 
built.

> 
> ---
> 
> ### **Summary of Positions**
> 
> **Flibble's position:**
> 
> * A Simulating Halt Decider (SHD) does not need to simulate to completion.
> * It can **use analysis to determine non-halting behavior early**, and
> halt the simulation accordingly.
> * Therefore, recursion into infinite self-reference is detected and does
> **not imply that the SHD itself fails to return**.
> 
> **Damon's position:**
> 
> * The SHD is logically inconsistent if it tries to be both:
> 
>    * A **simulator** of the input program **to determine its halting
> behavior**, and
>    * A **decider**, meaning it must always return a finite answer (1 for
> halts, 0 for non-halting).
> * If the input is truly non-halting, the simulation cannot halt and thus
> cannot return.
> * Hence, if **SHD halts and returns a result**, it cannot be doing a
> faithful simulation of a non-halting program—it would be logically broken.
> 
> ---
> 
> ### **Key Argument Points**
> 
> #### 1. **What counts as a valid simulation?**
> 
> * **Damon** argues that a **correct simulation must model the full
> behavior of the input program**, including potentially non-halting
> behavior. A SHD cannot simulate faithfully and still return if the
> simulated program is non-halting.
> * **Flibble** counters that **early symbolic analysis** is enough: if the
> SHD can detect an infinite loop pattern (e.g., recursive self-simulation),
> it may **abort the simulation and declare "non-halting"** without needing
> to recurse indefinitely.
> 
>> 🧠 *Flibble frames simulation as a partial tool, not the source of truth
> —the analysis result is.*
> 
> ---
> 
> #### 2. **The core of the disagreement: epistemology vs. ontology**
> 
> * Damon treats the SHD as needing to **ontologically match** the behavior
> of the program being simulated (i.e., model its behavior step-by-step).
> * Flibble approaches from an **epistemological** angle: the SHD's purpose
> is to *know* what the program would do, not to *be* that program.
> 
>> 🔁 *Damon believes an SHD can't be faithful if it stops early. Flibble
> says it's not required to be faithful in that sense—it must just return a
> correct answer.*
> 
> ---
> 
> #### 3. **Contradiction and paradox**
> 
> * Damon refers to a **contradiction**: if a decider returns “non-halting,”
> but only by aborting simulation, then it is **not** doing what it claims—
> simulating the non-halting behavior. That is, it returns an answer it
> couldn’t compute in the required way.
> * Flibble says this is a **false requirement**: the SHD isn’t obligated to
> run forever to decide a non-halting case. It only needs to **recognize the
> non-halting structure** (e.g., infinite regress) and return based on this.
> 
> ---
> 
> ### **Meta-commentary: Olcott’s Influence**
> 
> * Damon ends by saying: “It seems you have fallen for Olcott's insanity.”
> 
>    * This is a rhetorical move discrediting Flibble by associating his
> ideas with Olcott, who is frequently accused of **misunderstanding or
> misrepresenting** the halting problem.
>    * It's also an **ad hominem** by implication, suggesting guilt by
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