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Groups > comp.lang.c++ > #85151
| From | Jens Schweikhardt <usenet@schweikhardt.net> |
|---|---|
| Newsgroups | comp.lang.c, comp.lang.c++ |
| Subject | Re: H(P,P) is pure software engineering that correctly refutes the halting theorem |
| Followup-To | comp.lang.c |
| Date | 2022-07-13 21:08 +0000 |
| Message-ID | <jj8qhvF45m0U1@mid.individual.net> (permalink) |
| References | (3 earlier) <mOqdnRGdL5ZaM1H_nZ2dnUU7_8zNnZ2d@giganews.com> <tajvkl$13ac$1@gioia.aioe.org> <1tmdnWTZkrczuVP_nZ2dnUU7_8zNnZ2d@giganews.com> <t3qzK.380747$vAW9.26309@fx10.iad> <-bWdnc2EzYm6s1P_nZ2dnUU7_81g4p2d@giganews.com> |
Cross-posted to 2 groups.
Followups directed to: comp.lang.c
In comp.lang.c olcott <NoOne@nowhere.com> wrote:
[...]
# H(P,P) correctly predicts that its input cannot possibly terminate
# normally. (I have better words now).
Please excuse my ignorance, I'm very late to the discussion, if the
following has already been brought forward.
It is my understanding that a "working" halt decider can be used to
prove or disprove any math theorem that can be expressed as a program
that halts or doesn't halt, depending on whether the proposition is true
or false. Simple example: the Riemann Hypothesis that the non-trivial
zeros of the zeta function have real part 0.5.
A C program could halt if it finds a zero with real part not equal 0.5;
if it can't it will run forever (assuming arbitrary large memory for the
bignums).
int main (void) {
/* mycomplex: An arbitrary precision complex type. */
mycomplex zero = 0.0;
for (;;) {
zero = compute_next_zero(zero); /* elided for brevity */
if (realpart(zero) != 0.5)
break;
}
return 0;
}
So if your claim holds true, feed the program to your machine, if it
says "never halts" the RH is proven true, otherwise false. Too easy. But
how does the knowledge about all zeros come into your halt decider? And
abount all the trillions of other programs to prove or disprove a
theorem? What about some of the other non-tractable problems, such as
P=NP? Can we conceive a C program for this question?
I don't think any finite program could be such a general theorem prover
and therefore I am convinced you are chasing a ghost and there's
something you overlooked. I can't say what exactly, but I don't have to,
because the above to me is an reductio ad absurdum. Given the halting
problem could be solved, theorem proving becomes trivial immediately.
I am aware it's not a strict proof in the mathematical sense, but good
enough for me. It's like you are coming to a physicist with a new
perpetual motion machine. They will not spend time finding the exact
weak point in your contraption. They will simply reject it, like any
patent office worth their salt.
Regards,
Jens
--
Jens Schweikhardt http://www.schweikhardt.net/
SIGSIG -- signature too long (core dumped)
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Re: "C: Everyone's favourite programming language isn't a programming language" Albert Arkwright <Albert.Arkwright@gmail.com> - 2022-07-11 22:13 +0100
H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-11 18:14 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Freethinker <freethinker@mymail.com> - 2022-07-12 16:14 +0200
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-12 20:49 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-12 22:26 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-12 21:29 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-12 22:39 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-12 21:52 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 07:51 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 07:19 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-07-13 18:27 +0100
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 19:51 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 19:06 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 21:20 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 20:34 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 21:55 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 21:08 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 22:21 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 21:55 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-07-14 05:18 +0100
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 23:27 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-07-14 07:53 +0100
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-14 05:43 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-14 07:08 -0400
Re: H(P,P) is pure software engineering that correctly refutes the Muttley@dastardlyhq.com - 2022-07-14 16:06 +0000
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-13 23:29 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-07-14 07:52 +0100
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem olcott <NoOne@NoWhere.com> - 2022-07-14 05:49 -0500
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-14 07:12 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-07-14 17:48 +0100
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-14 07:07 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem om@iki.fi (Otto J. Makela) - 2022-07-18 17:51 +0300
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-13 22:29 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-07-13 19:41 -0700
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem - Olcott <polcott2@gmail.com> - 2022-07-13 20:03 -0700
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Richard Damon <Richard@Damon-Family.org> - 2022-07-14 21:55 -0400
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2022-07-14 22:04 -0700
Re: H(P,P) is pure software engineering that correctly refutes the halting theorem Jens Schweikhardt <usenet@schweikhardt.net> - 2022-07-13 21:08 +0000
Re: "C: Everyone's favourite programming language isn't a programming language" Juha Nieminen <nospam@thanks.invalid> - 2022-07-12 09:52 +0000
Re: "C: Everyone's favourite programming language isn't a programming language" Vir Campestris <vir.campestris@invalid.invalid> - 2022-07-12 11:27 +0100
Re: "C: Everyone's favourite programming language isn't a programming language" "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2022-07-12 13:01 -0700
Re: "C: Everyone's favourite programming language isn't a programming language" Manu Raju <MR@invalid.invalid> - 2022-07-12 22:19 +0100
Re: "C: Everyone's favourite programming language isn't a programming language" [Olcott] olcott <NoOne@NoWhere.com> - 2022-07-12 21:04 -0500
Re: "C: Everyone's favourite programming language isn't a programming language" Juha Nieminen <nospam@thanks.invalid> - 2022-07-13 10:02 +0000
Re: "C: Everyone's favourite programming language isn't a programming language" Muttley@dastardlyhq.com - 2022-07-13 15:24 +0000
Re: "C: Everyone's favourite programming language isn't a programming language" Manu Raju <MR@invalid.invalid> - 2022-07-13 19:00 +0100
Re: "C: Everyone's favourite programming language isn't a programming language" "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2022-07-13 15:31 -0700
Re: "C: Everyone's favourite programming language isn't a programming language" Bonita Montero <Bonita.Montero@gmail.com> - 2022-07-12 14:29 +0200
Re: "C: Everyone's favourite programming language isn't a programming language" Bonita Montero <Bonita.Montero@gmail.com> - 2022-07-12 14:46 +0200
Re: "C: Everyone's favourite programming language isn't a programming language" olcott <NoOne@NoWhere.com> - 2022-07-12 07:48 -0500
Re: "C: Everyone's favourite programming language isn't a programming language" Richard Damon <Richard@Damon-Family.org> - 2022-07-12 21:45 -0400
Re: "C: Everyone's favourite programming language isn't a programming language" Bonita Montero <Bonita.Montero@gmail.com> - 2022-07-17 08:18 +0200
Re: "C: Everyone's favourite programming language isn't a programming language" olcott <NoOne@NoWhere.com> - 2022-07-12 07:45 -0500
Re: "C: Everyone's favourite programming language isn't a programming language" Richard Damon <Richard@Damon-Family.org> - 2022-07-12 21:39 -0400
Re: "C: Everyone's favourite programming language isn't a programming language" olcott <NoOne@NoWhere.com> - 2022-07-12 07:45 -0500
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