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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Richard Heathfield Newsgroups: comp.theory Subject: Re: Turing Machine computable functions apply finite string transformations to inputs VERIFIED FACT Date: Tue, 29 Apr 2025 23:03:52 +0100 Organization: Fix this later Lines: 42 Message-ID: References: <65dddfad4c862e6593392eaf27876759b1ed0e69@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 30 Apr 2025 00:03:52 +0200 (CEST) Injection-Info: dont-email.me; posting-host="37e133e97ee7719e4a93228f44d9117b"; logging-data="2641487"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+f3GClVJxOXqv59D4Rysw4qZ7KXFcmtUCHN8w3Z6qTlQ==" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8P1FA7X3quHvk+AT5jpRuLgeOQA= Content-Language: en-GB In-Reply-To: Bytes: 3116 On 29/04/2025 22:38, olcott wrote: > > int DD() > { >   int Halt_Status = HHH(DD); >   if (Halt_Status) >     HERE: goto HERE; >   return Halt_Status; > } > > HHH is correct DD as non-halting BECAUSE THAT IS > WHAT THE INPUT TO HHH(DD) SPECIFIES. You're going round the same loop again. Either your HHH() is a universal termination analyser or it isn't. If it isn't, it's irrelevant to the Halting Problem, and we can ignore it. If it is, however, then we know that it doesn't work for all inputs, even if (as you claim) it works for one. > DD the Halting Problem counter-example input to HHH. > >> for the same reason we can't devise a universally accurate >> termination analyser that executes the code to see what happens. >> > > There is no evidence of that. Sure there is. Not just evidence, but an actual, rigorous, mathematical proof. -- Richard Heathfield Email: rjh at cpax dot org dot uk "Usenet is a strange place" - dmr 29 July 1999 Sig line 4 vacant - apply within