Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 11:05 PM, olcott wrote:

On 5/5/2025 9:56 PM, dbush wrote:

On 5/5/2025 10:51 PM, olcott wrote:

On 5/5/2025 9:27 PM, dbush wrote:

On 5/5/2025 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:

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Which starts with the assumption that an algorithm exists that performs the following mapping:
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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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DO COMPUTE THAT THE INPUT IS NON-HALTING
IFF (if and only if) the mapping FROM INPUTS
IS COMPUTED.

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i.e. it is found to map something other than the above function which is a contradiction.
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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.

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All you are doing is showing that you don't understand proof by contradiction,

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Not at all.

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Yes.
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The mapping is well defined.

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You don't even know that "well defined" means
that all of the steps have been specified.

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A mapping doesn't *have* steps. It's simply an association between an input domain and an output domain.
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 Computing the mapping does > have 100% totally specific steps

So you're assuming an algorithm exists that can compute the below mapping.
Then when a contradiction is reached, that proves the assumption false, as Linz and others proved and as you have *explicitly* agreed is correct.
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