Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory,sci.logic Subject: D correctly simulated by H cannot possibly halt --- templates and infinite sets Date: Tue, 28 May 2024 11:16:48 -0500 Organization: A noiseless patient Spider Lines: 39 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 28 May 2024 18:16:49 +0200 (CEST) Injection-Info: dont-email.me; posting-host="62ab2bf33c274f123184493b42753dfc"; logging-data="714481"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18MqFRr4OjsNuHuYpD8tKEt" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:uHorUYCkRS3d7kGYJbgQNglKqvw= Content-Language: en-US Bytes: 2041 typedef int (*ptr)(); // ptr is pointer to int function in C 00 int H(ptr p, ptr i); 01 int D(ptr p) 02 { 03 int Halt_Status = H(p, p); 04 if (Halt_Status) 05 HERE: goto HERE; 06 return Halt_Status; 07 } 08 09 int main() 10 { 11 H(D,D); 12 return 0; 13 } When Ĥ is applied to ⟨Ĥ⟩ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn *Formalizing the Linz Proof structure* ∃H ∈ Turing_Machines ∀x ∈ Turing_Machines_Descriptions ∀y ∈ Finite_Strings such that H(x,y) = Halts(x,x) *Here is the same thing applied to H/D pairs* ∃H ∈ C_Functions ∀D ∈ x86_Machine_Code_of_C_Functions such that H(D,D) = Halts(D,D) In both cases infinite sets are examined to see if any H exists with the required properties. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer