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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Tue, 6 May 2025 21:50:44 -0400
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On 5/6/2025 5:56 PM, olcott wrote:
> On 5/6/2025 4:12 PM, dbush wrote:
>> On 5/6/2025 4:57 PM, olcott wrote:
>>> On 5/6/2025 3:49 PM, dbush wrote:
>>>> On 5/6/2025 4:37 PM, olcott wrote:
>>>>> On 5/6/2025 3:22 PM, joes wrote:
>>>>>> Am Tue, 06 May 2025 13:05:15 -0500 schrieb olcott:
>>>>>>> On 5/6/2025 5:59 AM, Richard Damon wrote:
>>>>>>>> On 5/5/25 10:18 PM, olcott wrote:
>>>>>>>>> On 5/5/2025 8:59 PM, dbush wrote:
>>>>>>>>>> On 5/5/2025 8:57 PM, olcott wrote:
>>>>>>>>>>> On 5/5/2025 7:49 PM, dbush wrote:
>>>>>>
>>>>>>>>>>>>> DO COMPUTE THAT THE INPUT IS NON-HALTING IFF (if and only 
>>>>>>>>>>>>> if) the
>>>>>>>>>>>>> mapping FROM INPUTS IS COMPUTED.
>>>>>>>>>>>> i.e. it is found to map something other than the above function
>>>>>>>>>>>> which is a contradiction.
>>>>>>>>>>> The above function VIOLATES COMPUTER SCIENCE. You make no 
>>>>>>>>>>> attempt to
>>>>>>>>>>> show how my claim THAT IT VIOLATES COMPUTER SCIENCE IS 
>>>>>>>>>>> INCORRECT you
>>>>>>>>>>> simply take that same quote from a computer science textbook 
>>>>>>>>>>> as the
>>>>>>>>>>> infallible word-of-God.
>>>>>> What does it violate?
>>>>>>
>>>>>>>>>> All you are doing is showing that you don't understand proof by
>>>>>>>>>> contradiction,
>>>>>>>>> Not at all. The COMPUTER SCIENCE of your requirements IS WRONG!
>>>>>>>> No, YOU don't understand what Computer Science actually is talking
>>>>>>>> about.
>>>>>>> Every function computed by a model of computation must apply a 
>>>>>>> specific
>>>>>>> sequence of steps that are specified by the model to the actual 
>>>>>>> finite
>>>>>>> string input.
>>>>>
>>>>>> You are very confused. An algorithm or program computes a function.
>>>>>>
>>>>>
>>>>> Nothing computes a function unless it applies a specific
>>>>> set of rules to its actual input to derive its output.
>>>>> Anything that ignores its input is not computing a function.
>>>>>
>>>>
>>>> False.  Anything that correctly associates a function's input to a 
>>>> function's output for all elements of the function's domain does in 
>>>> fact compute that function.
>>>>
>>>>
>>>> For example, given this function:
>>>>
>>>> For all integers X and Y:
>>>> (X,Y) maps to 5
>>>>
>>>> This algorithm computes it:
>>>>
>>>> int foo(int X, int Y) { return 5; }
>>>>
>>>
>>> The rules that must be applied to the inputs
>>> are
>>
>> Anything that can associate the input with the output.
>>
> 
> WRONG!
> Any defined process that CAUSES an INPUT to be associated
> with an OUTPUT.
> 

If an algorithm exists that can generate the required output values for 
the given input values (such as the above algorithm foo and associated 
mapping), then how it gets the answer doesn't matter.  What matters is 
that it gets the answer.