Path: ...!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Termination analyzer defined ---RICHARD IS WRONG !!!
Date: Tue, 14 May 2024 09:15:34 -0500
Organization: A noiseless patient Spider
Lines: 40
Message-ID: <v1vrm6$7577$2@dont-email.me>
References: <v1me7i$1l6ut$1@dont-email.me> <v1nec4$1vb8i$1@dont-email.me>
 <v1o6p5$24f4c$2@dont-email.me> <v1pvj0$2knal$1@dont-email.me>
 <v1qi01$2on4q$2@dont-email.me> <v1qn4o$2pts6$1@dont-email.me>
 <v1qt92$2rdui$1@dont-email.me> <v1sl6o$3cg5n$1@dont-email.me>
 <v1tktb$3jv6d$1@dont-email.me> <v1vb6j$3ccc$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 14 May 2024 16:15:34 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="e9b15de5cbd4b611ca4438a3f5fabf94";
	logging-data="234727"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18OLZ91ITdUawkPWIkSvCKL"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:DRfMhBeLfJBVv6JLh7gQybzZ7Kc=
In-Reply-To: <v1vb6j$3ccc$1@dont-email.me>
Content-Language: en-US
Bytes: 2995

On 5/14/2024 4:34 AM, Mikko wrote:
> On 2024-05-13 18:07:37 +0000, Jeff Barnett said:
> 
>> On 5/13/2024 3:06 AM, Mikko wrote:
>>
>>> Anyway, if an analyzer can never tell whether a program terminates
>>> with every possible input then it is not a termination analyzer.
>>
>> I don't think the above is true in the way you meant it. Recall that 
>> the collection of all Turing machines with blank input tapes is the 
>> same set of computations as the collection with arbitrary input tapes. 
>> It's always possible to take any specific machine, T, and initial 
>> tape, I, and produce machine T' with blank initial input tape that is 
>> equivalent: T' initially writes I on its tape (say one character 
>> output per state in sequence) then continues with the set of states 
>> that comprises T.
>>
>> So it is obvious that a termination analyzer (AKA a halt decider) 
>> restricted to blank tape problems will do quite nicely and it is also 
>> quite obvious that no such entity exists.
> 
> You only discuss halting decisions with specific inputs. THerefore you say
> nothing about termination analyzers and don't show any mistake in my 
> comment.
> 

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

*My focus is even more narrow than that*

I only need to show that Linz embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ does correctly
determine the halt status of its input and the halting problem
proofs are refuted.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer