Re: Every sufficiently competent C programmer knows --- Semantic Property reiterated

On 3/13/2025 3:08 PM, olcott wrote:

On 3/13/2025 1:03 PM, dbush wrote:

On 3/13/2025 2:02 PM, olcott wrote:

On 3/13/2025 12:53 PM, dbush wrote:

On 3/13/2025 1:51 PM, olcott wrote:

On 3/13/2025 12:43 PM, dbush wrote:

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It is by the stipulated definition of a solution to the halting problem:
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Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
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A solution to the halting problem is an algorithm H that computes the following mapping:
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(<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
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WHEN THE STIPULATED DEFINITION OF [HALT DECIDER]
CONTRADICTS THE STIPULATED DEFINITION OF [DECIDER]
IT IS WRONG.
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Then it's a good thing we're talking about a solution to the halting problem instead of a decider.

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In other words you have no idea that the halting
problem requires a halt decider and a halt decider
must be a decider. Your ignorance is not my mistake.
>

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Your claim was that something that satisfies the definition of a solution to the halting problem doesn't satisfy the definition of a decider.  We fixed that by not calling it a decider.
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Happy?

 Yes I am happy because my doctor and I had a long conversation
that involved several good options to keep me alive longer.
 You already know that your reasoning is unsound unless you
can show that the halting problem never involved a halt decider.
 

The halting problem involves finding an algorithm H that satisfies these 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
So if such an H qualifies as a "decider" by your definition, that means the halting problem involves a decider.  If it doesn't qualify as a "decider" by your definition, that means the halting problem doesn't involve a decider.
Arguing, as you are, that the problem can be thrown out because you don't like the name it was given is, as you would say, quite nutty.