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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory,sci.logic Subject: Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets Date: Wed, 29 May 2024 20:09:10 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 30 May 2024 00:09:10 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2613824"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: Bytes: 8442 Lines: 181 On 5/29/24 8:01 PM, olcott wrote: > On 5/29/2024 6:47 PM, Richard Damon wrote: >> On 5/29/24 9:24 AM, olcott wrote: >>> On 5/29/2024 4:14 AM, Mikko wrote: >>>> On 2024-05-29 03:49:02 +0000, olcott said: >>>> >>>>> On 5/28/2024 10:38 PM, Richard Damon wrote: >>>>>> On 5/28/24 10:23 PM, olcott wrote: >>>>>>> On 5/28/2024 9:04 PM, Richard Damon wrote: >>>>>>>> On 5/28/24 12:16 PM, olcott 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       } >>>>>>>>> >>>>>>>>> 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) >>>>>>>> >>>>>>>> But since for x being the description of the H^ built from that >>>>>>>> H and y being the same, it turns out that no matter what answer >>>>>>>> H gives, it will be wrong. >>>>>>>> >>>>>>> >>>>>>> We have not gotten to that point yet this post is so that >>>>>>> you can fully understand what templates are and how they work. >>>>>> >>>>>> But note, x, being a Turing Machine, is NOT a "template" >>>>>> >>>>>> And H, isn't a "set of Turing Machines", but an arbitrary member >>>>>> of that set, so all we need to do is find a single x, y, possible >>>>>> determined as a function of H (so, BUILT from a template, but not >>>>>> a template themselves) that shows that particular H was wrong. >>>>>> >>>>>> >>>>>> That is basically what Linz does. >>>>>> >>>>>> Given a SPECIFIC (but arbitary) H, we can construct a specific H^ >>>>>> built from a template from H, that that H can not get right. >>>>>> >>>>>> All the other H's might get this input right, but we don't care, >>>>>> we have shown that for every H we >>>>>> >>>>>>> >>>>>>>> (And I think you have an error in your reference to Halts, I >>>>>>>> think you mean Halts(x,y) not Halts(x,x) >>>>>>>> >>>>>>> >>>>>>> Yes good catch. I was trying to model embedded_H / ⟨Ĥ⟩ >>>>>>> and then changed my mind to make it more general. >>>>>>> >>>>>>>>> >>>>>>>>> *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) >>>>>>>> >>>>>>>> Not the same thing. >>>>>>>> ∃H ∈ C_Functions >>>>>>>> is not equivalent to >>>>>>>> ∃H  ∈ Turing_Machines >>>>>>>> >>>>>>>> as there are many C_Functions that are not the equivalent of >>>>>>>> Turing Machines. >>>>>>>> >>>>>>> >>>>>>> The whole purpose here is to get you to understand what >>>>>>> templates are and how they reference infinite sets. >>>>>>> >>>>>> >>>>>> But the problem is that even in your formulation, H and D are, >>>>>> when doing the test, SPECIFIC PROGRAMS and not "templates" as >>>>>> Halts is defined on the domain of PROGRAMS. >>>>>> >>>>>> Similarly, a "Template" doesn't have a specific set of >>>>>> x86_Machine_Code_of_C_function, at least not one with defined >>>>>> behavior since if it tries to reference code outside of itself, >>>>>> then Halts of that just isn't defined, only Halts of that code + >>>>>> the specific machine deciding it. >>>>>> >>>>>>>> >>>>>>>>> >>>>>>>>> In both cases infinite sets are examined to see >>>>>>>>> if any H exists with the required properties. >>>>>>>>> >>>>>>>> >>>>>>>> Yes, but the logic of Turing Machines looks at them one at a >>>>>>>> time, and the input is a FULL INDEPENDENT PROGRAM. >>>>>>>> >>>>>>> >>>>>>> ∃H  ∈ Turing_Machines >>>>>>> That does not look at one machine it looks as an infinite set of >>>>>>> machines. I am very happy to find out that you were not playing head >>>>>>> games. Linz actually used the words that you referred to. >>>>>> >>>>>> while the ∃H part can create a set of machines, each element of >>>>>> that set is INDIVIDUALLY TESTED in the following conditions, so, >>>>>> when we get to your test  H(x,y) = Halts(x,x), each of H, x, y are >>>>>> individual members of the set, and we THEN collect the set of all >>>>>> of them. >>>>>> >>>>>> If we try to say >>>>>> ∃x ∈ Natural Numbers, such that  x+x = 3 >>>>>> we can't say that x is both 1 and 2 and thus as a set meet the >>>>>> requirement. For the conditions, each qualifier select a single >>>>>> prospective element, and those are tested to see if that meet the >>>>>> requirement. >>>>>> >>>>> >>>>> So it never was about any specific machine as Linz misleading words >>>>> seemed to indicate. It was always about examining each element of an >>>>> infinite set. >>>>> >>>>> Likewise: ∃H ∈ C_Functions is about examining each element >>>>> of an infinite set. A program template specifies a set of programs >>>>> the same way that an axiom schema specifies a set of axioms. >>>>> >>>>> I am very happy that the issue was the misleading words of Linz >>>>> and not you playing head games. >>>> >>>> In an inderect proof of an unversal claim the counter-hypothesis must >>>> be about one example. Then the proof is about that specific example >>>> until a contradiction is derived. >>>> >>> >>> Does there exist at least one example of this when the >>> infinite set of Turing_Machines have been examined? >>> >>> >>> Of the infinite set of Turing_Machines does there exist >>> at least one H that always gets this H(x,y) = Halts(x,y) >>> correctly for every {x,y} pair of the infinite set of {x,y} pairs? >> >> Then why was Linz able to create, for any specific H, an H^ that it >> get wrong? >> >> >>> >>> *Formalizing the Linz Proof structure* >>> ∃H  ∈ Turing_Machines >>> ∀x  ∈ Turing_Machines_Descriptions >>> ∀y  ∈ Finite_Strings >>> such that H(x,y) = Halts(x,y) >>> >> >> And since NO H, can get right the H^ built to contradict IT, that >> claim is proven false. >> > > YOU KEEP TRYING TO GET AWAY WITH CHANGING THE SUBJECT > THE ABOVE FORMALIZATION IS CORRECT > How? Since for EVERY H, Linz showed we can create an H^ (which creates the ========== REMAINDER OF ARTICLE TRUNCATED ==========