On 10/15/2025 11:38 AM, Kaz Kylheku wrote:>That the halting problem requires HHH to report on an
input that it not in its domain makes the halting problem
incoherent even at the purely mathematical level.
I made it clear to you that the input is constructable; thus the
situation can be made real, all the way to a physical realization.
You can build an input which incorporates a decision algorithm H, a
diagonal wrapper D, encode it into a finite string, and then have the
string processed by an implementation of algorithm H.
The string is a syntactically and semantically valid machine
representation and therefore lands squarely into the required domain.
Please see my new post it can be explained much
You've not had a genuinely new post in 15 years.
more succinctly: [The Halting Problem is Incoherent]
Without a shred of a doubt, your sixth-grade-level understanding of the
Halting Problem leaves it /looking/ incoherent to you.
The problem is probably that you believe that the self-references in the
problem are literal. So that if D is "the caller" of H, how can
it also be its input?
The references are representational.
The Halting Problem is ultimately about algorithms.
H is an algorithm, represented in some computational substrate.
The input string also contains the H algorithm, /separately
implemented/.
That's how D is the input and the caller of H. It's a caller of
its own implementation of H, not literally reaching outside of
the simulation to call its simulator.
You've further confused yourself by using C as an experimental
substrate, and using function pointers rather than finite string
representations, so that when DD is simulated by HHH, and calls HHH(DD),
it is using the pointer to the actual function that is simulating it.
--
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca
Les messages affichés proviennent d'usenet.