Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Fred. Zwarts" Newsgroups: comp.theory Subject: Re: Categorically exhaustive reasoning applied to the decision to abort Date: Wed, 27 Mar 2024 10:55:25 +0100 Organization: A noiseless patient Spider Lines: 69 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 27 Mar 2024 09:55:26 +0100 (CET) Injection-Info: dont-email.me; posting-host="3c03feda3a8cb3b751af5e283ec142d7"; logging-data="2912048"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/WDMm/1fSQneoqUodnS7Ii" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:FpEWeF5DAhWZcM1yXnFfEU7r+pQ= In-Reply-To: Content-Language: en-GB Bytes: 4468 Op 26.mrt.2024 om 15:43 schreef olcott: > On 3/26/2024 3:51 AM, Fred. Zwarts wrote: >> Op 25.mrt.2024 om 23:50 schreef olcott: >>> On 3/24/2024 11:42 AM, Mikko wrote: >>>> On 2024-03-24 03:39:12 +0000, olcott said: >>>> >>>>> On 3/23/2024 9:54 PM, immibis wrote: >>>>>> On 24/03/24 03:40, olcott wrote: >>>>>>> On 3/23/2024 9:34 PM, immibis wrote: >>>>>>>> On 24/03/24 03:15, olcott wrote: >>>>>>>>> On 3/23/2024 8:40 PM, immibis wrote: >>>>>>>>>> On 24/03/24 00:29, olcott wrote: >>>>>>>>>>> On 3/23/2024 5:58 PM, immibis wrote: >>>>>>>>>>>> On 23/03/24 16:02, olcott wrote: >>>>>>>>>>>>> (b) H(D,D) that DOES abort its simulation is correct >>>>>>>>>>>>>      (ABOUT THIS ABORT DECISION) >>>>>>>>>>>>>      because it would halt and all deciders must always halt. >>>>>>>>>>>> >>>>>>>>>>>> To be a decider it has to give an answer. >>>>>>>>>>>> >>>>>>>>>>>> To be a halt decider it has to give an answer that is the >>>>>>>>>>>> same as whether the direct execution of its input would halt. >>>>>>>>>>> >>>>>>>>>>> That would entail that >>>>>>>>>> >>>>>>>>>> Tough shit. That is the requirement. >>>>>>>>> >>>>>>>>> I proved otherwise in the parts you erased. >>>>>>>> >>>>>>>> You proved that the requirement is not actually the requirement? >>>>>>> >>>>>>> I proved that it cannot be a coherent requirement, it can still >>>>>>> be an incoherent requirement. Try and think it through for yourself. >>>>>> >>>>>> Every program/input pair either halts some time, or never halts. >>>>>> Determining this is a coherent requirement. >>>>> >>>>> That part is coherent. >>>> >>>> The part that this determination must be done by a Turing machine >>>> using descriptions of the program and input is coherent, too. >>>> >>> >>> Every decider is required by definition to only report on what >>> this input specifies. >>> >>> int sum(int x, int y){ return x + y; } >>> sum(3,4) is not allowed to report on the sum of 5 + 6 >>> even if you really really believe that it should. >>> >> >> Exactly! Therefore H(D,D), where D is based on H that aborts and >> returns false, so that D halts, should not return a report about >> another D that does not halt, even if you really really believe that >> it should. > > There is enough information for sum(3,4) to compute the sum of 3+4. > There is NOT enough information for sum(3,4) to compute the sum of 5+6. > > There is enough information for H1(D,D) to compute Halts(D,D). > There is NOT enough information for H(D,D) to compute Halts(D,D). > But it is possible to create a simulating sum decider that aborts sum and returns the sum of 5+6 and then claim that it is right, because it has not enough information to calculate 3+4. It is possible, but wrong. The only reason it has not enough information, is that it aborts prematurely. That makes the decision to abort wrong. This holds for H as well.