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: =?utf-8?B?UmU6IGVtYmVkZGVkX0ggYXBwbGllZCB0byDin6jEpOKfqSDin6jEpOKfqQ==?=
Date: Tue, 30 Jul 2024 09:37:58 +0300
Organization: -
Lines: 139
Message-ID: <v8a1o6$tvll$1@dont-email.me>
References: <v6rg65$32o1o$3@dont-email.me> <v734ct$mjis$2@dont-email.me> <056325e336f81a50f4fb9e60f90934eaac823d22@i2pn2.org> <v73gk2$obtd$1@dont-email.me> <e2958e7ea04d53590c79b53bfb4bc9dff468772b@i2pn2.org> <v742r2$s48s$2@dont-email.me> <210383b2ee318f68a96d94aec314ee8b93f79b7f@i2pn2.org> <v75u22$19j7l$4@dont-email.me> <fde630817c49562bc765bdbc98e16a1582bcad53@i2pn2.org> <v78mda$1smtm$2@dont-email.me> <v7d5cl$2t3ja$1@dont-email.me> <v7ds0o$30pvh$3@dont-email.me> <v7fs29$3f4g7$1@dont-email.me> <v7gd17$3hlc2$2@dont-email.me> <v7ikn4$1jv5$1@dont-email.me> <v7j2pg$3o7r$3@dont-email.me> <v7l3di$idv1$1@dont-email.me> <v7lnrf$luh0$1@dont-email.me> <v7niqp$13ghd$1@dont-email.me> <v7obbn$17h8r$1@dont-email.me> <v7qfm6$1m5ce$1@dont-email.me> <v7qvs3$1onhe$2@dont-email.me> <v7vnnn$2os1v$1@dont-email.me> <v80akb$2rabc$5@dont-email.me> <v82751$39qck$1@dont-email.me> <v82v0a$3dftr$4@dont-email.me> <v84tv8$3rmit$1@dont-email.me> <v88f8e$i7kl$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 30 Jul 2024 08:37:59 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="4618a86a1398dc578b50638a110088bd";
	logging-data="982709"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18511tt61S2+hGWW3MyTRXt"
User-Agent: Unison/2.2
Cancel-Lock: sha1:pGqj1Isi3FpZVscxgMK7L7AixHo=
Bytes: 7774

On 2024-07-29 16:16:13 +0000, olcott said:

> On 7/28/2024 3:02 AM, Mikko wrote:
>> On 2024-07-27 14:08:10 +0000, olcott said:
>> 
>>> On 7/27/2024 2:21 AM, Mikko wrote:
>>>> On 2024-07-26 14:08:11 +0000, olcott said:
>>>> 
>>>>> On 7/26/2024 3:45 AM, Mikko wrote:
>>>>>> On 2024-07-24 13:33:55 +0000, olcott said:
>>>>>> 
>>>>>>> On 7/24/2024 3:57 AM, Mikko wrote:
>>>>>>>> On 2024-07-23 13:31:35 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 7/23/2024 1:32 AM, 0 wrote:
>>>>>>>>>> On 2024-07-22 13:46:21 +0000, olcott said:
>>>>>>>>>> 
>>>>>>>>>>> On 7/22/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-07-21 13:34:40 +0000, olcott said:
>>>>>>>>>>>> 
>>>>>>>>>>>>> On 7/21/2024 4:34 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-07-20 13:11:03 +0000, olcott said:
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-07-19 14:08:24 +0000, olcott said:
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> When we use your incorrect reasoning we would conclude
>>>>>>>>>>>>>>>>> that Infinite_Loop() is not an infinite loop because it
>>>>>>>>>>>>>>>>> only repeats until aborted and is aborted.
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> You and your HHH can reason or at least conclude correctly about
>>>>>>>>>>>>>>>> Infinite_Loop but not about DDD. Possibly because it prefers to
>>>>>>>>>>>>>>>> say "no", which is correct about Infinte_loop but not about DDD.
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> *Because this is true I don't understand how you are not simply lying*
>>>>>>>>>>>>>>> int main
>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>    DDD();
>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> Calls HHH(DDD) that must abort the emulation of its input
>>>>>>>>>>>>>>> or {HHH, emulated DDD and executed DDD} never stop running.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> You are the lying one.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> If HHH(DDD) abrots its simulation and returns true it is correct as a
>>>>>>>>>>>>>> halt decider for DDD really halts.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>> 
>>>>>>>>>>>>> (b) We know that a decider is not allowed to report on the behavior
>>>>>>>>>>>>> computation that itself is contained within.
>>>>>>>>>>>> 
>>>>>>>>>>>> No, we don't. There is no such prohibition.
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> Turing machines never take actual Turing machines as inputs.
>>>>>>>>>>> They only take finite strings as inputs and an actual executing
>>>>>>>>>>> Turing machine is not itself a finite string.
>>>>>>>>>> 
>>>>>>>>>> The definition of a Turing machine does not say that a Turing machine
>>>>>>>>>> is not a finite string. It is an abstract mathematical object without
>>>>>>>>>> a specification of its exact nature. It could be a set or a finite
>>>>>>>>>> string. Its exact nature is not relevant to the theory of computation,
>>>>>>>>>> which only cares about certain properties of Turing machines.
>>>>>>>>>> 
>>>>>>>>>>> Therefore It is not allowed to report on its own behavior.
>>>>>>>>>> 
>>>>>>>>>> Anyway, that does not follow. The theory of Turing machines does not
>>>>>>>>>> prohibit anything.
>>>>>>>>>> 
>>>>>>>>>>> Another different TM can take the TM description of this
>>>>>>>>>>> machine and thus accurately report on its actual behavior.
>>>>>>>>>> 
>>>>>>>>>> If a Turing machine can take a description of a TM as its input
>>>>>>>>>> or as a part of its input it can also take its own description.
>>>>>>>>>> Every Turing machine can be given its own description as input
>>>>>>>>>> but a Turing machine may interprete it as something else.
>>>>>>>>>> 
>>>>>>>>> In this case we have two x86utm machines that are identical
>>>>>>>>> except that DDD calls HHH and DDD does not call HHH1.
>>>>>>>> 
>>>>>>>> That DDD calls HHH and DDD does not call HHH1 is not a difference
>>>>>>>> between two unnamed turing machines.
>>>>>>>> 
>>>>>>> 
>>>>>>> The same thing happens at the Peter Linz Turing Machine level
>>>>>>> I will provide that more difficult example if and only if you
>>>>>>> prove that you understand this one.
>>>>>> 
>>>>>> However, Peter Linz does not call taht same thing a difference.
>>>>> 
>>>>> We can call everything "late for dinner" with a unique integer
>>>>> index and the properties that I assert exist still exist.
>>>> 
>>>> That you can say all sorts stupid things does not mean that it be a
>>>> good idea to do so.
>>>> 
>>>> Some of the properties you assert exsit actually do exist, some don't.
>>>> 
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>> 
>>> 
>>> The above is merely simplified syntax for the top of page 3
>>> https://www.liarparadox.org/Linz_Proof.pdf
>>> The above is the whole original Linz proof.
>> 
>> And even more simplified semantics.
>> 
>>> (a) Ĥ copies its input ⟨Ĥ⟩
>>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
>>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (g) goto (d) with one more level of simulation
>>> 
>>> You are supposed to evaluate the above as a contiguous
>>> sequence of moves such that non-halting behavior is
>>> identified.
>> 
>> The above is an obvious tight loop of (d), (e), (f), and (g).
>> Its relevance (it any) to the topic of the discussion is not
>> obvious.
>> 
> 
> When we compute the mapping from the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> to the behavior specified by this input we know that embedded_H
> is correct to transition to Ĥ.qn.

The meaning of "correct" in this context is that if the transition of
embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn is correct if H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn but
incorrect otherwise.

-- 
Mikko