Rocksolid Light

Welcome to novaBBS (click a section below)

mail  files  register  newsreader  groups  login

Message-ID:  

Theory is gray, but the golden tree of life is green. -- Goethe


computers / comp.ai.philosophy / Concise refutation of halting problem proofs V16

SubjectAuthor
o Concise refutation of halting problem proofs V16olcott

1
Concise refutation of halting problem proofs V16

<Ds-dncRmJMxdgwj8nZ2dnUU7-bnNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/computers/article-flat.php?id=7598&group=comp.ai.philosophy#7598

 copy link   Newsgroups: comp.theory comp.ai.philosophy sci.logic sci.math
Followup: comp.theory
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.misty.com!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Wed, 17 Nov 2021 09:24:48 -0600
Date: Wed, 17 Nov 2021 09:24:46 -0600
MIME-Version: 1.0
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.3.1
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.math
Content-Language: en-US
Followup-To: comp.theory
From: NoO...@NoWhere.com (olcott)
Subject: Concise refutation of halting problem proofs V16
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Message-ID: <Ds-dncRmJMxdgwj8nZ2dnUU7-bnNnZ2d@giganews.com>
Lines: 55
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-oGdHjR0yA8dWzQY0uPDQ6Zh15JbGFmA2rUK9Q91eI7gCH1XSnEi9lRTD4X1nGFm7eQXaOBD53vwXvna!0RIIAdwbkNHB2/dWOvQxP7+FQgAp4dzWlZ8XpiTaBbYpwKKjYRAv0fhhap3AGj6O1PAODOYED0TH!iw==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 2626
 by: olcott - Wed, 17 Nov 2021 15:24 UTC

#include <stdint.h>
typedef void (*ptr)();

int H(ptr x, ptr y)
{ x(y); // direct execution of P(P)
return 1;
}

// Minimal essence of Linz(1990) Ĥ
// and Strachey(1965) P
int P(ptr x)
{ H(x, x);
return 1;
}

int main(void)
{ H(P, P);
}

We can determine the behavior of the input to H(P,P) for an infinite set
of different definitions of H by using categorically exhaustively
complete reasoning. There are only four categories of possible
definitions for H:

(1) H(P,P) simply executes its input: main() calls H(P,P) that calls
P(P) that calls H(P,P)...
(2) H(P,P) simulates its input.
(3) H(P,P) executes its input** and aborts this execution at some point.
**(a debugger could be used).
(4) H(P,P) simulates its input and aborts this simulation at some point.

Case (1) (complete source code is provided above) shows that P never
reaches its last instruction.
Case (2) a correct simulation of the input to H(P,P) must have
equivalent behavior to case (1).
Case (3) and (4) any sub-sequence of (1) and (2) can't have instructions
not included in (1) or (2).
Thus for cases (1)(2)(3)(4) P never reaches its last instruction.

For every H that
simulates or
executes its input and
aborts or
does not abort its input
P never reaches its last instruction.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

1
server_pubkey.txt

rocksolid light 0.9.7
clearnet tor