Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Tue, 4 Jun 2024 11:40:57 +0300
Organization: -
Lines: 74
Message-ID: <v3mjup$bu14$1@dont-email.me>
References: <v3501h$lpnh$1@dont-email.me> <v362eu$2d367$3@i2pn2.org> <v363js$vg63$2@dont-email.me> <v36803$2d368$3@i2pn2.org> <v368je$100kd$3@dont-email.me> <v373mr$2d367$5@i2pn2.org> <v37bpa$15n0b$1@dont-email.me> <v37i9p$lls$1@news.muc.de> <87y17smqnq.fsf@bsb.me.uk> <v37sap$18mfo$1@dont-email.me> <v38eq4$2foi0$1@i2pn2.org> <v38fe0$1bndb$1@dont-email.me> <v38g31$2foi0$11@i2pn2.org> <v38gi5$1bndb$3@dont-email.me> <v38ici$2fohv$2@i2pn2.org> <v38j17$1c8ir$2@dont-email.me> <v38jgo$2foi0$14@i2pn2.org> <v38jv9$1c8ir$4@dont-email.me> <v39agi$1jiql$1@dont-email.me> <v39v3h$1mtd9$5@dont-email.me> <v3b9kj$2im02$1@i2pn2.org> <v3bale$222n5$1@dont-email.me> <v3c1qo$25d0v$1@dont-email.me> <v3cpdu$297ao$3@dont-email.me> <v3k4ec$3ri9o$1@dont-email.me> <v3kfmt$3t5s5$9@dont-email.me> <v3kl6m$3ueeo$1@dont-email.me> <v3l1ib$5d3$6@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 04 Jun 2024 10:40:57 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="dce6fda481f9f7f7aa278ce7b31b5172";
	logging-data="391204"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+i5/gE7sn+pvz5jAxd7skG"
User-Agent: Unison/2.2
Cancel-Lock: sha1:rHbWDWWohggn24KDBF4VnPjyYFM=
Bytes: 4436

On 2024-06-03 18:20:59 +0000, olcott said:

> On 6/3/2024 9:49 AM, Mikko wrote:
>> On 2024-06-03 13:16:12 +0000, olcott said:
>> 
>>> On 6/3/2024 5:03 AM, Mikko wrote:
>>>> On 2024-05-31 15:13:02 +0000, olcott said:
>>>> 
>>>>> On 5/31/2024 3:30 AM, Mikko wrote:
>>>>>> On 2024-05-31 01:54:52 +0000, olcott said:
>>>>>> 
>>>>>>> On 5/30/2024 8:37 PM, Richard Damon wrote:
>>>>>>>> On 5/30/24 9:31 AM, olcott wrote:
>>>>>>>>> On 5/30/2024 2:40 AM, Mikko wrote:
>>>>>>>>>> On 2024-05-30 01:15:21 +0000, olcott said:
>>>>>>> 
>>>>>>>>>>> x <is> a finite string Turing machine description that SPECIFIES 
>>>>>>>>>>> behavior. The term: "representing" is inaccurate.
>>>>>>>>>> 
>>>>>>>>>> No, x is a description of the Turing machine that specifies the behaviour
>>>>>>>>>> that H is required to report.
>>>>>>>>> 
>>>>>>>>> That is what I said.
>>>>>>>> 
>>>>>>>> Note, the string doesn't DIRECTLY specify behavior, but only indirectly 
>>>>>>>> as a description/representation of the Turing Mach
>>>>>>>> 
>>>>>>> 
>>>>>>> The string directly SPECIFIES behavior to a UTM or to
>>>>>>> any TM based on a UTM.
>>>>>> 
>>>>>> An UTM interpretes the string as a specification of behaviour
>>>>> 
>>>>> YES, exactly !!!
>>>>> 
>>>>>> and another Turing machine may interprete likewise. But in a
>>>>>> different context the interpretation is different.
>>>>>> 
>>>>> 
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>> 
>>>>> When embedded_H <is> a UTM or <is> a halting computation based on a
>>>>> UTM then the ⟨Ĥ⟩ ⟨Ĥ⟩ input to embedded_H SPECIFIES that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly
>>>>> simulated by embedded_H cannot possibly reach its own simulated final
>>>>> state at ⟨Ĥ.qn⟩.
>>>> 
>>>> There is no requirement to follow the pecifications by embedded_H.
>>> 
>>> 
>>> In other words embedded_H can simply play bingo and never halt and 
>>> still correctly decide the halt status of its input?
>> 
>> Not of the input text but of the machine and input that the text
>> describes. The input to H contains enough information that the
>> machine can be constructed and run with the input. If the prediction
>> by H differs from the actual execution of the machine the prediction
>> is wrong and H is not a halt decider.
>> 
> 
> 
> int sum(int x, int y) { return x + y; }
> sum(2,3) cannot return the sum of 5 + 6.
> 
> DD correctly simulated by HH does have provably
> different behavior than DD(DD) so HH is is not
> allowed to report on the behavior of DD(DD).

Show the proof (or a pointer to the beginning of the proof).

-- 
Mikko