Re: Yet another contribution to the P-NP question

On Fri, 27 Sep 2024 22:42:31 +0000, Ben Bacarisse wrote:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>

On 27/09/2024 00:34, Ben Bacarisse wrote:

nnymous109@gmail.com (nnymous109) writes:
>

Also, I did not know this yesterday, but alternatively, you can access
the document directly through the following link:
https://figshare.com/articles/preprint/On_Higher_Order_Recursions_25SEP2024/27106759?file=49414237

I am hoping that this is a joke.  If it is a joke, then I say well done
sir (or madam)[*].
But I fear it is not a joke, in which case I have a problem with the
first line.  If you want two of the states to be symbols (and there are
points later on that confirm that this is not a typo) then you need to
explain why early on.  You are free to define what you want, but a paper
that starts "let 2 < 1" will have the reader wrong-footed from the
start.

>
You mean q_accept and q_reject?  It looks like they are just to
represent
the accept and reject states, not tape symbols?  Calling them symbols is
like calling q_0 a symbol, which seems harmless to me - is it just that
you
want to call them "labels" or something other than "symbols"?

>
Later he/she writes
>
   (Omega U {q_accept, q_reject})*
>
where * is, presumably, the Kleene closure.  Omega is the set of
non-blank tape symbols of the TMs under discussion so these states are
used to make "strings" with other tape symbols.
>
I agree that what the states actually are is irrelevant, but that two of
them are later used like this is presumably important.
>

I don't fully get the notation though - e.g. it seems to me that the TMs
have tape symbols and states, but I don't see any state transition
table!

>
Right, but that's line 2 and I was starting at line 1!
>
I thought it might be joke because of the way the author just piles
definition on definition using bizarre notations like integral symbols
but apparently not.

Okay, Ben. Please allow me to try again.
I'm not completely sure how to use USENET to reply to portions of
replies, so I will try to answer some of your queries here since the
other reply is much longer.
I don't actually use the Turing machines formalism at all in my
arguments until about point 22, so throughout the document I'm not
thinking about Turing machine states and Turing machine symbols and
Turing machine configurations, at all.
But in trying to discuss with others, I tend to just cast the entire
argument in the language of Turing machines, since I felt that that
would be more familiar. Maybe I shouldn't have done that.
It's probably more accurate to say that I am trying to come up with a
string re-writing model of computation as you pick up on. So everything
is a string, and everything that can be used to form a string is a
symbol, so there's no semantic difference between the following strings:
0 0 1 0 0 0 1
1 1 q_a r_e 0 0 2 3 d
q_accept q_reject q_accept 1 1 q_reject 0 0 0 d f g
Then we have some rules that tell us to replace substrings of any given
string with another string. That's the entire recursion idea (and yes,
we could do this with a Turing machine, but I'm asking us to forget
about Turing machines momentarily).
Also, rather than do a wall of text like last time, I think I should
pause and ask for criticisms here, and then answer them/proceed as is
necessary.