Re: Halting Problem proofs appear to be bogus!

Subject	Re: Halting Problem proofs appear to be bogus!
Newsgroups	comp.theory, comp.ai.philosophy, comp.software-eng, sci.math.symbolic
References	(1 earlier) <871r7ys7pd.fsf@bsb.me.uk> <INqdnZRsHJyUCWz9nZ2dnUU7-afNnZ2d@giganews.com> <87sg0dolgt.fsf@bsb.me.uk> <Afadnb2qftX9Zm_9nZ2dnUU7-QXNnZ2d@giganews.com> <877dhommoc.fsf@bsb.me.uk>
From	olcott <NoOne@NoWhere.com>
Date	2021-07-19 10:10 -0500
Message-ID	<CLWdnehcAdpqCGj9nZ2dnUU7-R2dnZ2d@giganews.com> (permalink)

Cross-posted to 4 groups.

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On 7/17/2021 8:32 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
> ...
>> I only skimmed the above, I skipped most of the words.
> 
> Good plan.  You really don't want to know what I said!  I've cut it
> since you don't care about details.  Let's stick with the big picture.
> 
>> int main() { P(P); } is computationally equivalent to Ĥ(⟨Ĥ⟩).
> 
> Yes.  P(P) halts (according to you).  H(P,P) == 0 (according to you).
> That is wrong (according to everyone but you).
> 

Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
if M applied to wM halts, and

Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
if M applied to wM does not halt

Unless the simulating halt decider embedded at state Ĥ.qx aborts the 
simulation of its input at some point its input never halts thus proving 
beyond all possible doubt that the input that was aborted is correctly 
decided as never halting.

When a computation only stops running because its simulation was aborted 
this counts as a computation that never halts.

-- 
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre 
minds." Einstein

Thread

Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 09:13 -0500
  Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-19 10:10 -0500
    Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-20 09:24 -0500

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