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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Flibble=E2=80=99s_Leap=3A_Why_Behavioral_Divergence?=
 =?UTF-8?Q?_Implies_a_Type_Distinction_in_the_Halting_Problem?=
Date: Sun, 11 May 2025 12:54:54 -0500
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On 5/11/2025 12:49 PM, dbush wrote:
> On 5/11/2025 1:44 PM, olcott wrote:
>> On 5/11/2025 12:34 PM, dbush wrote:
>>> On 5/11/2025 1:14 PM, olcott wrote:
>>>> On 5/11/2025 11:54 AM, dbush wrote:
>>>>> On 5/11/2025 12:49 PM, olcott wrote:
>>>>>> The category error is actually the fact that everyone
>>>>>> here expects a termination analyzer to report on behavior
>>>>>> other than the behavior that its input finite string
>>>>>> actually specifies.
>>>>>
>>>>> That's because it's whether or not the algorithm described by the 
>>>>> input halts when executed directly.
>>>>>
>>>>> No one cares what "the behavior that its input finite string 
>>>>> specifies" because that's not what we asked about.
>>>>
>>>> int sum(int x, int y) { return x + y ; }
>>>> when you ask about the sum of 5 + 7 using sum(3,2)
>>>> you are asking the wrong question.
>>>>
>>>> HHH reports on the behavior that DDD specifies.
>>>> sum reports on the sum that its inputs specify.
>>>>
>>>
>>> Category error.  (2,3) is not (5,7), but (DDD) is (DDD).
>>>
>>
>> DDD correctly emulated by HHH SPECIFIES RECURSIVE EMULATION
>> DDD correctly emulated by HHH1 DOES NOT SPECIFY RECURSIVE EMULATION
>>
>>
>>
> 
> What DDD "specifies" is irrelevent.  What matters is what algorithm is 
> described by DDD, 

Specifies means provides every single step
of the entire execution trace.

Describes means to mention some details.
We could "describe" DDD by saying that DDD
has the name DDD.

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