Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Fred. Zwarts" Newsgroups: comp.theory Subject: Re: Infinite set of HHH/DDD pairs --- truisms Date: Mon, 22 Jul 2024 20:16:59 +0200 Organization: A noiseless patient Spider Lines: 74 Message-ID: References: <60a1c2490e9bd9a5478fd173a20ed64d5eb158f9@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 22 Jul 2024 20:17:00 +0200 (CEST) Injection-Info: dont-email.me; posting-host="ab0c04790edcdbcdbb42536aede3135b"; logging-data="803715"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/R8eaxnUAEii3uuBVa/eE8" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:2U0lMapFB/oU9WTruvt/2TtPk90= Content-Language: en-GB In-Reply-To: Bytes: 5126 Op 22.jul.2024 om 19:51 schreef olcott: > On 7/22/2024 12:45 PM, Fred. Zwarts wrote: >> Op 22.jul.2024 om 17:08 schreef olcott: >>> On 7/22/2024 9:32 AM, joes wrote: >>>> Am Mon, 22 Jul 2024 09:13:33 -0500 schrieb olcott: >>>>> On 7/22/2024 3:01 AM, Mikko wrote: >>>>>> On 2024-07-21 13:50:17 +0000, olcott said: >>>>>>> On 7/21/2024 4:38 AM, Mikko wrote: >>>>>>>> On 2024-07-20 13:28:36 +0000, olcott said: >>>>>>>>> On 7/20/2024 3:54 AM, Mikko wrote: >>>>>>>>>> On 2024-07-19 14:39:25 +0000, olcott said: >>>>>>>>>>> On 7/19/2024 3:51 AM, Mikko wrote: >>>> >>>>>>>>>> Anyway you did not say that some HHHᵢ can simulate the >>>>>>>>>> corresponding DDDᵢ to its termination. And each DDDᵢ does >>>>>>>>>> terminate, whether simulated or not. >>>> >>>> >>>>>>> Then DDD correctly simulated by any pure function HHH cannot >>>>>>> possibly >>>>>>> reach its own return instruction and halt, therefore every HHH is >>>>>>> correct to reject its DDD as non-halting. >>>>>> That does not follow. It is never correct to reject a halting >>>>>> comoputation as non-halting. >>>>> In each of the above instances DDD never reaches its return >>>>> instruction >>>>> and halts. This proves that HHH is correct to report that its DDD >>>>> never >>>>> halts. >>>> It can't return if the simulation of it is aborted. >>>> >>>>> Within the hypothetical scenario where DDD is correctly emulated by >>>>> its >>>>> HHH and this HHH never aborts its simulation neither DDD nor HHH ever >>>>> stops running. >>>> In actuality HHH DOES abort simulating. >>>> >>>>> This conclusively proves that HHH is required to abort the >>>>> simulation of >>>>> its corresponding DDD as required by the design spec that every >>>>> partial >>>>> halt decider must halt and is otherwise not any kind of decider at >>>>> all. >>>> Like Fred recognised a while ago, you are arguing as if HHH didn't >>>> abort. >>>> >>>>> That HHH is required to abort its simulation of DDD conclusively >>>>> proves >>>>> that this DDD never halts. >>>> You've got it the wrong way around. >>>> >>> >>> I am talking about hypothetical possible ways that HHH could be encoded. >>> (a) HHH(DDD) is encoded to abort its simulation. >>> (b) HHH(DDD) is encoded to never abort its simulation. >>> >>> Therefore (a) is correct and (b) is incorrect according to the >>> design requirements for HHH that it must halt. >> >> Both are incorrect. An HHH, when encoded to abort does not need to be >> aborted when simulated, because it already halts on its own. > > When no HHH(DDD) ever aborts its input then HHH never halts > conclusively proving that some HHH must abort its input. > Indeed, but dreaming of an HHH that does not abort is irrelevant when we consider a HHH that is encoded to abort. The HHH that aborts, simulates itself: the HHH that aborts. No HHH that does not abort is involved. When a HHH aborts, it is not needed to abort its simulation, because it will halt by its own. So for any HHH, whether it aborts or not, we can say: HHH cannot possibly simulate itself correctly up to the end.