XPost: comp.theory, comp.software-eng, sci.logic
On 1/29/2022 11:34 AM, Ben Bacarisse wrote:
Richard Damon <Richard@Damon-Family.org> writes:
And the 'actual behavior of its actual inputs' is DEFINED to be what
the computation the input actually does when run as an independent
machine, or what a UTM will do when simulating that input.
If that isn't the meaning you are using, then you are just lying that
you are working on the halting problem, which is what seems to be the
case. (That you are lying that is).
It is certainly true that PO is not addressing the halting problem. He
has been 100% clear that false is, in his "opinion", the correct result
for at least one halting computation. This is not in dispute (unless
he's retracted that and I missed it).
THIS POINT ADDRESSES THE KEY QUESTION
Which state does Ĥ applied to ⟨Ĥ⟩ transition to correctly ?
The following simplifies the syntax for the definition of the Linz
Turing machine Ĥ, it is now a single machine with a single start state.
A copy of Linz H is embedded at Ĥ.qx.
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
There are no finite number of steps of the pure simulation of ⟨Ĥ⟩
applied to ⟨Ĥ⟩ by embedded_H such that this simulated input meets the
Linz definition of halting:
computation that halts … the Turing machine will halt whenever it enters
a final state. (Linz:1990:234)
Therefore it is correct to say that the input to embedded_H specifies a sequence of configurations that never halts.
https://www.researchgate.net/publication/358009319_Halting_problem_undecidability_and_infinitely_nested_simulation_V3
To you and I, this means that he's not working on the halting problem,
but I am not sure you can say he is lying about that. For one thing,
how can he be intending to deceive (a core part of lying) when he's been clear the he accepts the wrong answer as being the right one? If
someone claims to be working on "the addition problem", and also claims
that 2+2=5 is correct, it's hard to consider either claim to be a lie.
The person is just deeply confused.
But what sort of confused can explain this nonsense? I think the answer
lies in PO's background. The "binary square root" function is not
computable as far as a mathematician is concerned because no TM can halt with, say, sqrt(0b10) on the tape. But to an engineer, the function
poses no problem because we can get as close as we like. If
0b1.01101010000 is not good enough, just add more digits.
The point is I think PO does not know what a formal, mathematical
problem really is. To him, anything about code, machines or programs is about solving an engineering problem "well enough" -- with "well enough"
open to be defined by PO himself.
More disturbing to me is that he is not even talking about Turing
machines, again as evidenced by his own plain words. It is not in
dispute that he claims that two (deterministic) TMs, one an identical
copy of the other, can transition to different states despite both being presented with identical input. These are not Turing machines but Magic machines, and I can't see how any discussion can be had while the action
of the things being considered is not a simple function of the input and
the state transition graph.
THIS POINT ADDRESSES A SIDE ISSUE NOT RELEVANT TO THE KEY QUESTION:
What are the details of how ⟨Ĥ⟩ applied to ⟨Ĥ⟩ behaves?
H and embedded_H are not identical, one has an infinite loop appended to
its accept state.
I will not tolerate digression into this side issue until after mutual agreement is achieved on the first point. Until then these side issues
are no more than a dishonest dodge distraction away from the main point.
This is why I stopped replying. While there are things to say about
PO's Other Halting problem (principally that even the POOH problem can't
be solved), I had nothing more to say while the "machines" being
discussed are magic.
--
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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