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: I have always been correct about emulating termination analyzers --- PROOF
Date: Tue, 22 Oct 2024 10:13:57 +0300
Organization: -
Lines: 30
Message-ID: <vf7jbl$1cr7h$1@dont-email.me>
References: <ves6p1$2uoln$1@dont-email.me> <3232d8a0cc7b5d4bba46321bf682c94573bf1b7c@i2pn2.org> <vesemu$2v7sh$1@dont-email.me> <a9fb95eb0ed914d0d9775448c005111eb43f2c5b@i2pn2.org> <veslpf$34ogr$1@dont-email.me> <647fe917c6bc0cfc78083ccf927fe280acdf2f9d@i2pn2.org> <vetq7u$3b8r2$1@dont-email.me> <522ecce215e636ddb7c9a1f75bff1ba466604cc5@i2pn2.org> <veuvt9$3hnjq$1@dont-email.me> <87634d01e18903c744d109aaca3a20b9ce4278bb@i2pn2.org> <vev8gg$3me0u$1@dont-email.me> <eb38c4aff9c8bc250c49892461ac25bfccfe303f@i2pn2.org> <vf051u$3rr97$1@dont-email.me> <e3f28689429722f86224d0d736115e4d1895299b@i2pn2.org> <vf1hun$39e3$1@dont-email.me> <dedb2801cc230a4cf689802934c4b841ae1a29eb@i2pn2.org> <vf1stu$8h0v$1@dont-email.me> <592109c757262c48aaca517a829ea1867913316b@i2pn2.org> <vf37qt$fbb3$1@dont-email.me> <vf5430$sjvj$1@dont-email.me> <vf5mat$v6n5$4@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 22 Oct 2024 09:13:57 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="a7aeb215248b43d962fe1f69aee1679e";
	logging-data="1469681"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18kPxujjUXmuJh0kQh5Gjpm"
User-Agent: Unison/2.2
Cancel-Lock: sha1:f82K/wVMwKYnHqRNICR+Tzqvm1o=
Bytes: 2705

On 2024-10-21 13:52:28 +0000, olcott said:

> On 10/21/2024 3:41 AM, Mikko wrote:
>> On 2024-10-20 15:32:45 +0000, olcott said:
>> 
>>> The actual barest essence for formal systems and computations
>>> is finite string transformation rules applied to finite strings.
>> 
>> Before you can start from that you need a formal theory that
>> can be interpreted as a theory of finite strings.
> 
> Not at all. The only theory needed are the operations
> that can be performed on finite strings:
> concatenation, substring, relational operator ...

You may try with an informal foundation but you need to make sure
that it is sufficicently well defined and that is easier with a
formal theory.

> The minimal complete theory that I can think of computes
> the sum of pairs of ASCII digit strings.

That is easily extended to Peano arithmetic.

As a bottom layer you need some sort of logic. There must be unambifuous
rules about syntax and inference.

-- 
Mikko