Path: ...!weretis.net!feeder9.news.weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D(D) simulated by H presents non-halting behavior to H
Date: Tue, 7 May 2024 16:23:39 -0500
Organization: A noiseless patient Spider
Lines: 133
Message-ID: <v1e64r$3fq5a$1@dont-email.me>
References: <v18e32$1vbql$1@dont-email.me> <v1avuv$2lks2$1@dont-email.me>
 <v1b7gl$2ndka$1@dont-email.me> <v1cla9$34iis$1@dont-email.me>
 <v1d2mi$9f72$11@i2pn2.org> <v1di1h$3b2m5$1@dont-email.me>
 <v1dtdv$3dqg4$1@dont-email.me> <v1du2i$3dt7u$1@dont-email.me>
 <v1e3k6$3fa85$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 07 May 2024 23:23:40 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="1fe47412d5222aa086f42d5af46fe483";
	logging-data="3664042"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19N6VZau+ZFunYnlSi9ICCl"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:MNSR5k+Ll+D/qfGvoYDITbA8DXo=
Content-Language: en-US
In-Reply-To: <v1e3k6$3fa85$2@dont-email.me>
Bytes: 6674

On 5/7/2024 3:40 PM, Fred. Zwarts wrote:
> Op 07.mei.2024 om 21:05 schreef olcott:
>> On 5/7/2024 1:54 PM, Fred. Zwarts wrote:
>>> Op 07.mei.2024 om 17:40 schreef olcott:
>>>> On 5/7/2024 6:18 AM, Richard Damon wrote:
>>>>> On 5/7/24 3:30 AM, Mikko wrote:
>>>>>> On 2024-05-06 18:28:37 +0000, olcott said:
>>>>>>
>>>>>>> On 5/6/2024 11:19 AM, Mikko wrote:
>>>>>>>> On 2024-05-05 17:02:25 +0000, olcott said:
>>>>>>>>
>>>>>>>>> The x86utm operating system: https://github.com/plolcott/x86utm 
>>>>>>>>> enables
>>>>>>>>> one C function to execute another C function in debug step mode.
>>>>>>>>> Simulating Termination analyzer H simulates the x86 machine 
>>>>>>>>> code of its
>>>>>>>>> input (using libx86emu) in debug step mode until it correctly 
>>>>>>>>> matches a
>>>>>>>>> correct non-halting behavior pattern proving that its input 
>>>>>>>>> will never
>>>>>>>>> stop running unless aborted.
>>>>>>>>>
>>>>>>>>> Can D correctly simulated by H terminate normally?
>>>>>>>>> 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 }
>>>>>>>>>
>>>>>>>>> *Execution Trace*
>>>>>>>>> Line 11: main() invokes H(D,D);
>>>>>>>>>
>>>>>>>>> *keeps repeating* (unless aborted)
>>>>>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates 
>>>>>>>>> D(D)
>>>>>>>>>
>>>>>>>>> *Simulation invariant*
>>>>>>>>> D correctly simulated by H cannot possibly reach past its own 
>>>>>>>>> line 03.
>>>>>>>>>
>>>>>>>>> The above execution trace proves that (for every H/D pair of the
>>>>>>>>> infinite set of H/D pairs) each D(D) simulated by the H that 
>>>>>>>>> this D(D)
>>>>>>>>> calls cannot possibly reach past its own line 03.
>>>>>>>>
>>>>>>>> When you say "every H/D pair" you should specify which set of pairs
>>>>>>>> you are talking about. As you don't, your words don't mean 
>>>>>>>> anything.
>>>>>>>>
>>>>>>>
>>>>>>> Every H/D pair in the universe where D(D) is simulated by the
>>>>>>> same H(D,D) that D(D) calls. This involves 1 to ∞ steps of D
>>>>>>> and also includes zero to ∞ recursive simulations where H
>>>>>>> H simulates itself simulating D(D).
>>>>>>
>>>>>> "In the universe" is not a set. In typical set theories like ZFC 
>>>>>> there
>>>>>> is no universal set.
>>>>>
>>>>
>>>> This template defines an infinite set of finite string H/D pairs 
>>>> where each D(D) that is simulated by H(D,D) also calls this same 
>>>> H(D,D).
>>>>
>>>> These H/D pairs can be enumerated by the one to ∞ simulated steps of 
>>>> D and involve zero to ∞ recursive simulations of H simulating itself 
>>>> simulating D(D). Every time Lines 1,2,3 are simulated again defines
>>>> one more level of recursive simulation.
>>>>
>>>> 1st element of H/D pairs 1 step  of D  is simulated by H
>>>> 2nd element of H/D pairs 2 steps of D are simulated by H
>>>> 3rd element of H/D pairs 3 steps of D are simulated by H
>>>>
>>>> 4th element of H/D pairs 4 steps of D are simulated by H
>>>> this begins the first recursive simulation at line 01
>>>>
>>>> 5th element of H/D pairs 5 steps of D are simulated by
>>>> next step of the first recursive simulation at line 02
>>>>
>>>> 6th element of H/D pairs 6 steps of D are simulated by
>>>> last step of the first recursive simulation at line 03
>>>>
>>>> 7th element of H/D pairs 7 steps of D are simulated by H
>>>> this begins the second recursive simulation at line 01
>>>
>>> Is this the definition of the infinite set of H? We can think of many 
>>> more simulations that only these.
>>
>> This template defines an infinite set of finite string H/D pairs where
>> each D(D) that is simulated by H(D,D) also calls this same H(D,D).
>>
> 
> This template does not define any H. So, 

The template specifies an infinite set of finite string H/D pairs
where each D(D) that is simulated by H(D,D) also calls this same H(D,D).

> it does not define a H/D pair 

When by "define" you mean provide all of the source-code of H
you are right. That is not what I meant. I cannot provide
all of the source-code for an infinite set of functions.

> either. The enumeration might be part of a definition for a set of H 
> functions, but the question was whether the enumeration defines the 
> whole set. If so, why is it limited to this enumeration?
> 

The template specifies an infinite set of finite string H/D pairs
where each D(D) that is simulated by H(D,D) also calls this same H(D,D).

This includes implementations of H that play tic-tac-toe.
It does not include any D not simulated by H.
It does not include and D(D) that does not call this H.

>>> In particular since the H as presented is not a pure function,
>>> but uses hidden inputs. If hidden inputs are allowed, it is easy
>>> to construct very different H functions, e.g., H functions for
>>> which the number of steps differ at each simulation level.
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer