Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 07:46:33 -0400
Organization: A noiseless patient Spider
Lines: 184
Message-ID: <vvfh6o$10b0m$2@dont-email.me>
References: <GE4SP.47558$VBab.42930@fx08.ams4> <vvamqc$o6v5$4@dont-email.me>
 <vvan7q$o4v0$1@dont-email.me> <ts5SP.113145$_Npd.41800@fx01.ams4>
 <vvao8p$o4v0$2@dont-email.me> <vvav61$vtiu$5@dont-email.me>
 <vvckjd$2krkf$1@dont-email.me> <vvd8o9$34l9k$4@dont-email.me>
 <b2aa4a06c49960ef30db2f18da40a9319808fce5@i2pn2.org>
 <vvee2r$89sm$1@dont-email.me>
 <dabb21b6077fbe3c2496ef84da115e6db6370bc4@i2pn2.org>
 <vveher$89u0$10@dont-email.me> <vvehl4$etf4$4@dont-email.me>
 <vvep45$lgd3$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 07 May 2025 13:46:33 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="3013d96e0ac4b7dd359f7afe652f4ce0";
	logging-data="1059862"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+Zejg0kKMIfV2g2qq6R9O2"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:/hohUAiISCo7KOHKNvzY0zlglXU=
In-Reply-To: <vvep45$lgd3$2@dont-email.me>
Content-Language: en-US

On 5/7/2025 12:55 AM, olcott wrote:
> On 5/6/2025 9:48 PM, dbush wrote:
>> On 5/6/2025 10:44 PM, olcott wrote:
>>> On 5/6/2025 9:34 PM, Richard Damon wrote:
>>>> On 5/6/25 9:47 PM, olcott wrote:
>>>>> On 5/6/2025 5:43 PM, Richard Damon wrote:
>>>>>> On 5/6/25 11:10 AM, olcott wrote:
>>>>>>> On 5/6/2025 4:26 AM, Mikko wrote:
>>>>>>>> On 2025-05-05 18:14:25 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 5/5/2025 11:16 AM, dbush wrote:
>>>>>>>>>> On 5/5/2025 12:13 PM, Mr Flibble wrote:
>>>>>>>>>>> On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:
>>>>>>>>>>>
>>>>>>>>>>>> On 5/5/2025 11:51 AM, olcott wrote:
>>>>>>>>>>>>> On 5/5/2025 10:17 AM, Mr Flibble wrote:
>>>>>>>>>>>>>> What constitutes halting problem pathological input:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Input that would cause infinite recursion when using a 
>>>>>>>>>>>>>> decider of the
>>>>>>>>>>>>>> simulating kind.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Such input forms a category error which results in the 
>>>>>>>>>>>>>> halting problem
>>>>>>>>>>>>>> being ill-formed as currently defined.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>> I prefer to look at it as a counter-example that refutes 
>>>>>>>>>>>>> all of the
>>>>>>>>>>>>> halting problem proofs.
>>>>>>>>>>>>
>>>>>>>>>>>> Which start with the assumption that the following mapping 
>>>>>>>>>>>> is computable
>>>>>>>>>>>> and that (in this case) HHH computes it:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>>>>>>>>> instructions) X
>>>>>>>>>>>> described as <X> with input Y:
>>>>>>>>>>>>
>>>>>>>>>>>> A solution to the halting problem is an algorithm H that 
>>>>>>>>>>>> computes the
>>>>>>>>>>>> following mapping:
>>>>>>>>>>>>
>>>>>>>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed 
>>>>>>>>>>>> directly
>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when 
>>>>>>>>>>>> executed
>>>>>>>>>>>> directly
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> int DD()
>>>>>>>>>>>>> {
>>>>>>>>>>>>>     int Halt_Status = HHH(DD);
>>>>>>>>>>>>>     if (Halt_Status)
>>>>>>>>>>>>>       HERE: goto HERE;
>>>>>>>>>>>>>     return Halt_Status;
>>>>>>>>>>>>> }
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://github.com/plolcott/x86utm
>>>>>>>>>>>>>
>>>>>>>>>>>>> The x86utm operating system includes fully operational HHH 
>>>>>>>>>>>>> and DD.
>>>>>>>>>>>>> https://github.com/plolcott/x86utm/blob/master/Halt7.c
>>>>>>>>>>>>>
>>>>>>>>>>>>> When HHH computes the mapping from *its input* to the 
>>>>>>>>>>>>> behavior of DD
>>>>>>>>>>>>> emulated by HHH this includes HHH emulating itself 
>>>>>>>>>>>>> emulating DD. This
>>>>>>>>>>>>> matches the infinite recursion behavior pattern.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thus the Halting Problem's "impossible" input is correctly 
>>>>>>>>>>>>> determined
>>>>>>>>>>>>> to be non-halting.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Which is a contradiction.  Therefore the assumption that the 
>>>>>>>>>>>> above
>>>>>>>>>>>> mapping is computable is proven false, as Linz and others 
>>>>>>>>>>>> have proved
>>>>>>>>>>>> and as you have *explicitly* agreed is correct.
>>>>>>>>>>>
>>>>>>>>>>> The category (type) error manifests in all extant halting 
>>>>>>>>>>> problem proofs
>>>>>>>>>>> including Linz.  It is impossible to prove something which is 
>>>>>>>>>>> ill- formed
>>>>>>>>>>> in the first place.
>>>>>>>>>>>
>>>>>>>>>>> /Flibble
>>>>>>>>>>
>>>>>>>>>> All algorithms either halt or do not halt when executed 
>>>>>>>>>> directly. Therefore the problem is not ill formed.
>>>>>>>>>
>>>>>>>>> When BOTH Boolean RETURN VALUES are the wrong answer
>>>>>>>>> THEN THE PROBLEM IS ILL-FORMED. Self-contradiction must
>>>>>>>>> be screened out as semantically incorrect.
>>>>>>>>
>>>>>>>> Irrelevant. One of the boolean values (the one not returned) is the
>>>>>>>> right one as can be determined e.g. with an UTM.
>>>>>>>>
>>>>>>>>>> You only get something that appears that way when a false 
>>>>>>>>>> assumption is made, namely that the halting function is 
>>>>>>>>>> computable.
>>>>>>>>>
>>>>>>>>> The mapping from the input HHH(DD) finite string of
>>>>>>>>> machine code to DOES SPECIFY RECURSIVE EMULATION
>>>>>>>>> THAT WOULD PREVENT DD FROM EVER HALTING.
>>>>>>>>
>>>>>>>> No, it does not. HHH returns 0 and DD halts.
>>>>>>>>
>>>>>>>
>>>>>>> You can't show the detailed steps of the execution
>>>>>>> trace of DD emulated by HHH (according to the rules
>>>>>>> of the x86 language) where DD halts because you are wrong.
>>>>>>
>>>>>> Because a trace of DD correctly emulatd by HHH doesn't exist as 
>>>>>> HHH doesn't correctly emulate DD
>>>>>>
>>>>>
>>>>> Show what the execution trace of DD emulated by HHH
>>>>> according to the rules of the x86 language should be
>>>>>
>>>>
>>>> Since HHH doesn't do that, 
>>>
>>> and you cannot possibly point out what the correct
>>> steps should be
>>
>>
>> The steps that UTM / HHH1 takes that HHH does not, 
> 
> which are the steps of DD emulated by HHH
> according to the rules of the x86 language

False, as you yourself have admitted on the record that it does not:


On 5/5/2025 8:24 AM, dbush wrote:
 > On 5/4/2025 11:03 PM, dbush wrote:
 >> On 5/4/2025 10:05 PM, olcott wrote:
 >>> On 5/4/2025 7:23 PM, Richard Damon wrote:
 >>>> But HHH doesn't correct emulated DD by those rules, as those rules
 >>>> do not allow HHH to stop its emulation,
 >>>
 >>> Sure they do you freaking moron...
 >>
 >> Then show where in the Intel instruction manual that the execution of
 >> any instruction other than a HLT is allowed to stop instead of
 >> executing the next instruction.
 >>
 >> Failure to do so in your next reply, or within one hour of your next
 >> post on this newsgroup, will be taken as you official on-the-record
 >> admission that there is no such allowance and that HHH does NOT
 >> correctly simulate DD.
 >
 > Let the record show that Peter Olcott made the following post in this
 > newsgroup after the above message:
 >
 > On 5/4/2025 11:04 PM, olcott wrote:
 >  > D *WOULD NEVER STOP RUNNING UNLESS*
 >  > indicates that professor Sipser was agreeing
 >  > to hypotheticals AS *NOT CHANGING THE INPUT*
 >  >
 >  > You are taking
 >  > *WOULD NEVER STOP RUNNING UNLESS*
 >  > to mean *NEVER STOPS RUNNING* that is incorrect.
 >
 > And has made no attempt after over 9 hours to show where in the Intel
 > instruction manual that execution is allowed to stop after any
========== REMAINDER OF ARTICLE TRUNCATED ==========