Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mike Terry <news.dead.person.stones@darjeeling.plus.com>
Newsgroups: comp.theory
Subject: Re: Incorrect requirements --- Computing the mapping from the input
 to HHH(DD)
Date: Mon, 12 May 2025 01:38:10 +0100
Organization: A noiseless patient Spider
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In-Reply-To: <vvqln4$g8ck$5@dont-email.me>

On 11/05/2025 18:11, Richard Heathfield wrote:
> On 11/05/2025 17:44, olcott wrote:
>> Any yes/no question where both yes and no are the
>> wrong answer is an incorrect polar question.
> 
> Either DD stops or it doesn't (once it's been hacked around to get it to compile and after we've 
> leeched out all the dodgy programming).

Done that.  It still stops.

> 
> If the computer cannot correctly decide whether or not DD halts, 

The decider says it doesn't stop..

> we have an undecidable computation, 

No no, that doesn't make sense.  DD stops, and there are lots of partial halt deciders that will 
decide that particular input correctly.  PO's DD isn't "undecidable".

No single computation can be undecidable, considered on its own!  There are only two possibilities: 
it halts or it doesn't.  In either case there is a decider which decides that /one specific input/ 
correctly.  By extension, any finite number of computations is decidable - we just have a giant 
switch statement followed by returning halts/neverhalts as appropriate.  If the input domain has 
just n inputs, there are 2^n trivial deciders that together cater for every combination of each 
input halting or never halting.  One of those deciders is a correct decider for that (finite domain) 
problem.

The HP is asking for a TM (or equiv.) that correctly decides EVERY (P,I) in its one finite 
algorithm.  That is what is proven impossible.  The trick of having a big switch statement no longer 
works because there are infinitely many possible inputs.

Decidability for just one single input is trivial and not intersting.

> and therefore some computations are undecidable, so Turing's conclusion was right. Who knew? (Apart 
> from practically everybody else, I mean.)


Mike.