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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Fri, 14 Mar 2025 13:51:45 -0400
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On 3/14/2025 11:51 AM, olcott wrote:
> On 3/14/2025 10:04 AM, wij wrote:
>> On Fri, 2025-03-14 at 09:35 -0500, olcott wrote:>>
>>> void DDD()
>>> {
>>>     HHH(DDD);
>>>     return;
>>> }
>>>
>>> DDD correctly simulated by HHH cannot possibly reach
>>> its own "return" instruction in any finite number of
>>> correctly simulated steps.
>>>
>>> That you are clueless about the semantics of something
>>> as simple as a tiny C function proves that you are not
>>> competent to review my work.
>>>
>>
>> https://en.wikipedia.org/wiki/Halting_problem
>> In computability theory, the halting problem is the problem of 
>> determining, from a description of an
>> arbitrary computer program and an input, whether the program will 
>> finish running, or continue to run
>> forever.
>>
>> That means: H(D)=1 if D() halts and H(D)=0 if D() does not halt.
>>
>> But, it seems you don't understand English, as least as my level, ....
>>
>>
>>
> 
> void DDD()
> {
>    HHH(DDD);
>    return;
> }
> 
> The only difference between HHH and HHH1 is that they are
> at different locations in memory. DDD simulated by HHH1
> has identical behavior to DDD() directly executed in main().
> 
> The semantics of the finite string input DDD to HHH specifies


That it will halt when executed directly

> 
> The semantics of the finite string input DDD to HHH1 specifies

That it will halt when executed directly

> 
> When HHH(DDD) reports on the behavior that its input finite
> string specifies it can only correctly report non-halting.
> 


False.  The finite string specifies a computation that halts when 
executed directly, as per the requirements:


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


> When HHH(DDD) is required to report on behavior other than
> the behavior that its finite string specifies HHH is not
> a decider thus not a halt decider.
> 


In other words, you're claiming an H where H(X) reports what X will do 
when executed directly is not a decider.  What term would you use to 
describe it, then?


> All deciders are required to compute the mapping from
> their input finite string to the semantic or syntactic property
> that this string specifies. Deciders return true when this
> string specifies this property otherwise they return false.
> 
> 

And the finite string DDD specifies a computation that halts when 
executed directly.