XPost: comp.theory, sci.logic, sci.math

On 11/24/2021 2:56 PM, André G. Isaak wrote:

On 2021-11-24 13:41, olcott wrote:

On 11/24/2021 1:48 PM, André G. Isaak wrote:

On 2021-11-24 12:36, olcott wrote:

On 11/24/2021 1:19 PM, André G. Isaak wrote:

But the halting *function* doesn't involve any decider. It is simply
a mapping from computations to their halting status.

Again, reread what I wrote. Mathematical functions don't involve
"invoking" anything. They are simply mappings, i.e. sets of ordered
pairs.

The job of a halt *decider* is to compute the mappings contained in
that function.

a decider always maps finite strings to accept reject states.

Yes, it maps finite strings to accepting or rejecting states, but in
doing so it computes a *function*. I am asking you to think about what
that function is, not about the decider itself. The function is prior to
the decider.

Please explain how the ordered pair ((P, P), true) involves any sort of reference, let alone 'pathological self reference'. That is the relevant element of the halting *function* which your decider allegedly computes.

You keep simply ignoring the fact the an input with pathological
self-reference has different behavior than one that does not.
You keep trytng to simply assume away verified facts.

Again, I am trying to get you to focus on the halting *function*, not on
your H. We can come back to your H once you demonstrate that you
understand what the distinction between the halting function and a halt decider is, but you seem determined not to understand this.

The mapping to a digraph contains cycles that do not exist for other
inputs.

Linz demonstrates that this isn't possible. *YOU'VE* demonstrated
that this isn't possible but you keep trying to change the rules of
the game so you can maintain that your 'decider' is somehow getting
the right answer when it is not. A halt decider must compute the
halting function as described above.

Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms,

No, they are not. A computable function is a function for which it is
*possible* to construct an algorithm. But a computable function is
*not* an algorithm. It is simply a set of ordered pairs.

Once again, I ask, why is it that when people attempt to correct you
on your misuse of terminology you insist on doubling down rather than
carefully reading what is said to try to understand the distinction
between terms that is being brought to your attention?

André

You are correcting an encyclopedia.
deciders are a specific type of computable function that
maps finite strings to accept reject states.

No. I am correcting you.

Deciders are a specific type of turing machine which *computes* a
computable function. Something which computes a function is not the same thing as that function.

A function is a mapping.

A computation is an alogorithm.

A computable function is a function for which an algorithm exists for computing that function.

A decider is related to some computable function. That doesn't make it a computable function.

André

The sequence of 1 to N configurations specified by the input to H(X, Y)
cannot be correctly construed as anything other than the sequence of 1
to N steps of the (direct execution, x86 emulation or UTM simulation of
this input).

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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