Path: ...!feeds.phibee-telecom.net!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory,sci.logic Subject: Re: D correctly simulated by pure function H cannot possibly reach its, own line 06 --- Linz proof Date: Sun, 26 May 2024 12:54:56 -0500 Organization: A noiseless patient Spider Lines: 85 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 26 May 2024 19:54:57 +0200 (CEST) Injection-Info: dont-email.me; posting-host="b67ec24a85de95a55e6b4d0cc81926c3"; logging-data="3689715"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+o+e3hfr5AkOkBZyrfyciq" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:TbwLEBOYzgj5132uz1bibTjGaVw= Content-Language: en-US In-Reply-To: Bytes: 5522 On 5/26/2024 12:48 PM, Richard Damon wrote: > On 5/26/24 1:26 PM, olcott wrote: >> On 5/26/2024 12:16 PM, Richard Damon wrote: >>> On 5/26/24 1:01 PM, olcott wrote: >>>> On 5/26/2024 11:31 AM, Richard Damon wrote: >>>>> On 5/26/24 10:13 AM, olcott wrote: >>>>>> On 5/26/2024 6:43 AM, Richard Damon wrote: >>>>>> >>>>>> 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       } >>>>>> >>>>>> >>>>>>> Because, as I have said, the answer and reasoning changes >>>>>>> depending on what you acknowledged are the implications of your >>>>>>> stipulations. For instance, if your actual understanding of being >>>>>>> a "Pure Function" is that the program is the equivalent of a >>>>>>> Turing Machine, then we need to add a strictness to the >>>>>>> definition that isn't normally used for just "Pure Functions", >>>>>>> like accessing value of registers like the program counter or >>>>>>> stack pointer might not be allowed in some cases. (which breaks >>>>>>> you H). >>>>>>> >>>>>> >>>>>> Since we can see (and you already agreed) that D correctly simulated >>>>>> by pure simulator H remains stuck in infinite recursive simulation >>>>>> then >>>>>> we also know that D never reaches its own line 06 and halts in less >>>>>> than an infinite number of correctly simulated steps. >>>>> >>>>> But it depends on what H actually does, which you refuse to agree to. >>>>> >>>> >>>> When I specify that D is correctly simulated by pure function H, that >>>> means that H is a pure simulator that stops simulating D after some >>>> finite number of correctly simulated steps. There is absolutely nothing >>>> else that needs to be known about H besides this. >>>> >>> >>> And, do you accept that this exact description means that H is NOT >>> the computational equivalent of a Turing Machine, and that this >>> simulation doesn't prove that its input is not a non-halting program? >>> >> >> In other words you are saying that it is 100% totally impossible to >> adapt an actual UTM so that it stops simulating after a finite number of >> steps. > > Yep, at least and have it still be a UTM. > > IMPOSSIBLE BY DEFINITION. *Yet not otherwise impossible at all* When Ĥ is applied to ⟨Ĥ⟩ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn Thus when we hypothesize that embedded_H is an exact UTM then we see that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final state of ⟨Ĥ.qn⟩ even in an infinite number of simulated steps. From this we can definitively conclude that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final state of ⟨Ĥ.qn⟩ in less than an infinite number of simulated steps. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer