XPost: comp.theory, sci.logic, sci.math
On 3/16/2022 9:03 PM, Richard Damon wrote:
On 3/16/22 9:51 PM, olcott wrote:
On 3/16/2022 8:36 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 3/16/2022 8:16 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
On 3/12/2022 8:55 PM, Ben Bacarisse wrote:
André G. Isaak <agisaak@gm.invalid> writes:
On 3/12/2022 5:57 PM, André G. Isaak wrote:
So what string, according to you, encodes the computation Ĥ >>>>>>>>>> applied
to ⟨Ĥ⟩? If these two "different" computations don't have separate
encodings as strings then they are not, in fact, different >>>>>>>>>> computations at all.
No Comment?
I know you've been asked this question before and have consistently >>>>>>>> ignored it. According to a recent post of yours that constitutes >>>>>>>> justification for a repetitive all-caps temper tantrum!
I once tried to get a direct answer to this question. I asked 12 >>>>>>> times
in consecutive posts but never got one.
Later, on the related question of whether ⟨Ĥ⟩ ⟨Ĥ⟩ encodes a halting
computation I got this dazzling display of equivocation:
"When it is construed as input to H then ⟨Ĥ⟩ ⟨Ĥ⟩ encodes a
halting
computation.
When it is construed as input to Ĥ.qx then ⟨Ĥ⟩ ⟨Ĥ⟩ DOES NOT
encode a
halting computation."
Bear in mind that at time, PO's machines were magic: two
identical state
transition functions could entail transitions to different states >>>>>>> when
presented with identical inputs. He has since backed off from
some of
these remarks, but it never exactly clear which previous claims
he would
now accept were wrong.
None-the-less...
You mean you won't comment on the above but would rather present new >>>>> junk about BASIC. Oh well... I can't stop you.
None-the-less none of what you have ever said shows that I am
incorrect.
Ah! So from your point of view I did not point out an error in the post >>> you replied to. That means you /still/ think that:
"When it is construed as input to H then ⟨Ĥ⟩ ⟨Ĥ⟩ encodes a halting
computation. When it is construed as input to Ĥ.qx then ⟨Ĥ⟩ ⟨Ĥ⟩ DOES
NOT encode a halting computation."
THIS IS THE ONLY POINT THAT MATTERS
THIS IS THE ONLY POINT THAT MATTERS
THIS IS THE ONLY POINT THAT MATTERS
THIS IS THE ONLY POINT THAT MATTERS
That the simulated input: ⟨Ĥ⟩ ⟨Ĥ⟩ to embedded_H would never reach the
final state of this simulated input in any finite number of steps of
correct simulation by embedded_H conclusively proves that a mapping
from this input to the reject state of embedded_H is correct.
Except that 'correct simulation by embedded_H' only has meaning if
embedded_H is actually
embedded_H has all of the functionality of a UTM and is able to
(a) Perfectly simulate its input as if it was a UTM.
(b) Watch the behavior of this simulated input.
(c) Match the behavior of this simulated input with infinite behavior
patterns.
As soon as an infinite behavior pattern is correctly matched embedded_H
has complete proof that its input would never reach the final state of
this input, thus the input never halts even if aborted.
Since we can see that there is an infinite behavior pattern we can see
that a transition to the embedded_H reject state would be correct.
This by itself refutes the Linz proof because the Linz proof concludes
that Ĥ applied to ⟨Ĥ⟩ results in a contradiction. (see direct quote below) and there is no actual contradiction.
</Linz:1990:320>
Now Ĥ is a Turing machine, so that it will have some description in Σ*,
say ŵ . This string, in addition to being the description of Ĥ can also
be used as input string. We can therefore legitimately ask what would
happen if Ĥ is applied to ŵ .
…
The contradiction tells us that our assumption of the existence of H,
and hence the assumption of the decidability of the halting problem,
must be false.
</Linz:1990:320>
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)