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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Thu, 13 Mar 2025 08:54:23 -0500
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On 3/13/2025 7:03 AM, dbush wrote:
> On 3/13/2025 12:05 AM, olcott wrote:
>> On 3/12/2025 9:49 PM, dbush wrote:
>>> On 3/12/2025 10:41 PM, olcott wrote:
>>>> On 3/12/2025 7:56 PM, dbush wrote:
>>>>> On 3/12/2025 8:41 PM, olcott wrote:>>
>>>>>>
>>>>>> NOT WHEN IT IS STIPULATED THAT THE BEHAVIOR BEING
>>>>>> MEASURED IS 
>>>>>
>>>>>
>>>>> The direct execution of DDD 
>>>>
>>>> is proven to be different than the behavior of DDD
>>>> emulated by HHH according to the semantics of the
>>>> x86 language.
>>>>
>>>
>>> Which is not what a solution to the halting problem is stipulated to 
>>> compute:
>>>
>>>
>>
>> Unless you look more deeply into these things and
>> realize that it is the semantic property of the
>> (computation encoded as a) finite string that Rice's
>> Theorem is based on.
> 
> And that semantic property is the direct execution of the program 
> described by the input.
> 
> 
>>
>>> Given any algorithm (i.e. a fixed immutable sequence of instructions) 
>>> X described as <X> with input Y:
>>>
>>
>> The finite string pair DDD/HHH specifies a different
>> computation than the finite string pair DDD/HHH1.
>>
> 
> False.  DDD is the description of the algorithm <DDD> 

There is no vague description of an algorithm when we examine
these things concretely. We get rid of this vagueness when we
switch from some unspecified Turing Machine description
(not even knowing the details of the language) to actual x86
machine code.

With x86 machine code when N steps of DDD are emulated by
HHH according to the semantics of the x86 language

_DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov  ebp,esp  ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add  esp,+04
[00002182] 5d         pop  ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]

We get a DDD that cannot possibly reach its own machine address
0000217f. There is no conditional code in DDD that prevents
it from calling HHH(DDD) each time it is recursively emulated.

> which includes the 
> fixed code of the function DDD, the fixed code of the function HHH (i.e. 
> HHH is part of the input), and the fixed code of everything it calls 
> down to the OS level.
> 
> So HHH(DDD) and HHH1(DDD) are both being passed the same program 
> description and are therefore required to both compute the same mapping:
> 

When you ignore the fact that DDD calls HHH in recursive
emulation and does not call HHH1 in recursive emulation
you are a liar.

Richard understands that lying can get him sent to Hell
and does not care.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer