Path: ...!news-out.netnews.com!s1-1.netnews.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!nntp.club.cc.cmu.edu!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory,sci.logic Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?= =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?= Date: Mon, 27 May 2024 21:24:21 -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: Tue, 28 May 2024 01:24:22 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2405839"; 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: X-Received-Bytes: 11751 Bytes: 11922 Lines: 253 On 5/27/24 9:04 PM, olcott wrote: > On 5/27/2024 7:48 PM, Richard Damon wrote: >> On 5/27/24 8:26 PM, olcott wrote: >>> On 5/27/2024 7:17 PM, Richard Damon wrote: >>>> On 5/27/24 8:08 PM, olcott wrote: >>>>> On 5/27/2024 5:44 PM, Richard Damon wrote: >>>>>> On 5/27/24 6:32 PM, olcott wrote: >>>>>>> On 5/27/2024 4:21 PM, Richard Damon wrote: >>>>>>>> On 5/27/24 3:45 PM, olcott wrote: >>>>>>>>> On 5/27/2024 11:33 AM, Richard Damon wrote: >>>>>>>>>> On 5/27/24 12:22 PM, olcott wrote: >>>>>>>>>>> On 5/27/2024 10:58 AM, Richard Damon wrote: >>>>>>>>>>>> On 5/27/24 11:46 AM, olcott wrote: >>>>>>>>>>>>> On 5/27/2024 10:25 AM, Richard Damon wrote: >>>>>>>>>>>>>> On 5/27/24 11:06 AM, 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       } >>>>>>>>>>>>> >>>>>>>>>>>>> The above template refers to an infinite set of H/D pairs >>>>>>>>>>>>> where D is >>>>>>>>>>>>> correctly simulated by either pure simulator H or pure >>>>>>>>>>>>> function H. This >>>>>>>>>>>>> was done because many reviewers used the shell game ploy to >>>>>>>>>>>>> endlessly >>>>>>>>>>>>> switch which H/D pair was being referred to. >>>>>>>>>>>>> >>>>>>>>>>>>> *Correct Simulation Defined* >>>>>>>>>>>>>     This is provided because many reviewers had a different >>>>>>>>>>>>> notion of >>>>>>>>>>>>>     correct simulation that diverges from this notion. >>>>>>>>>>>>> >>>>>>>>>>>>>     A simulator is an x86 emulator that correctly emulates >>>>>>>>>>>>> 1 to N of the >>>>>>>>>>>>>     x86 instructions of D in the order specified by the x86 >>>>>>>>>>>>> instructions >>>>>>>>>>>>>     of D. This may include M recursive emulations of H >>>>>>>>>>>>> emulating itself >>>>>>>>>>>>>     emulating D. >>>>>>>>>>>> >>>>>>>>>>>> And how do you apply that to a TEMPLATE that doesn't define >>>>>>>>>>>> what a call H means (as it could be any of the infinite set >>>>>>>>>>>> of Hs that you can instantiate the template on)? >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> *Somehow we got off track of the subject of this thread* >>>>>>>>>> >>>>>>>>>> I note that YOU keep on switching between your C program and >>>>>>>>>> Turing Machines. >>>>>>>>>> >>>>>>>>>> Note, per the implications that you implicitly agreed to (by >>>>>>>>>> not even trying to refute) the two systems are NOT equivalents >>>>>>>>>> of each other. >>>>>>>>>> >>>>>>>>> >>>>>>>>> (1) I think you are wrong. I have not seen any of your >>>>>>>>> reasoning that was not anchored in false assumptions. >>>>>>>>> Your make fake rebuttal is to change the subject. >>>>>>>>> >>>>>>>>> (2) It does not matter my proof is anchored in the Linz >>>>>>>>> proof and the H/D pairs are only used to have a 100% concrete >>>>>>>>> basis to perfectly anchor things such as the correct meaning >>>>>>>>> of D correctly simulated by H so that people cannot get away >>>>>>>>> with claiming that an incorrect simulation is correct. >>>>>>>>> >>>>>>>>> int main() { D(D); } IS NOT THE BEHAVIOR OF D CORRECTLY >>>>>>>>> SIMULATED BY H. >>>>>>>>> One cannot simply ignore the pathological relationship between >>>>>>>>> H and D. >>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> When Ĥ is applied to ⟨Ĥ⟩ >>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>>>>>>>>> >>>>>>>>>>>   Ĥ copies its own Turing machine description: ⟨Ĥ⟩ >>>>>>>>>>>   then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input. >>>>>>>>>>> >>>>>>>>>>> For the purposes of the above analysis we hypothesize that >>>>>>>>>>> embedded_H is either a UTM or a UTM that has been adapted >>>>>>>>>>> to stop simulating after a finite number of steps of simulation. >>>>>>>>>> >>>>>>>>>> And what you do mean by that? >>>>>>>>>> >>>>>>>>>> Do you hypothesize that the original H was just a pure UTM, >>>>>>>>> >>>>>>>>> The original proof does not consider the notion of a simulating >>>>>>>>> halt decider so I have to begin the proof at an earlier stage >>>>>>>>> than any definition of H. >>>>>>>> >>>>>>>> The biggest problem is that the input to the Turing machine >>>>>>>> decider H is the description of a Turing Machine H^, which is a >>>>>>>> SPECIFIC machine, >>>>>>> >>>>>>> When you say "specific machine" you don't mean anything like a >>>>>>> 100% completely specified sequence of state transitions encoded >>>>>>> as a single unique finite string. >>>>>> >>>>>> Mostly. >>>>>> >>>>>> There doesn't need to be a unique finite string, but it is a 100% >>>>>> completely specified state transition/tape operation table. >>>>>> >>>>> >>>>> When Ĥ is applied to ⟨Ĥ⟩ >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>>> >>>>> In other words Linz did not prove that there are no set >>>>> of state transitions specified by ⊢* that derives the >>>>> correct halt status of ⟨Ĥ⟩ ⟨Ĥ⟩. >>>>> >>>>> He only said there there is one specific machine that >>>>> gets the wrong answer. >>>>> >>>> >>>> He STARTS with a proof that one specific (but arbitrary) machine >>>> gets the wrong answer. >>>> >>>> Then he shows that the same proof can be applied to ANY such machine >>>> (becaue the proof didn't depend on any specific details of the >>>> machine, just the general properties of that machine) >>>> >>>> I guess you don't understand how to do categorical proofs. >>>> >>> >>> I totally do. Can you please write down the >>> "completely specified state transition/tape operation table." >>> of this specific (thus uniquely identifiable) machine I would >>> really like to see it. >>> >> >> But it was proven that no such machine exists! >> >> Remember, the proof starts with the hypothetical that such a machine >> exists. Such a machine WOULD HAVE a completely specified state >> transition/tape operation table. >> > > That is not what you said. > >>>>> There doesn't need to be a unique finite string, but it is a 100% > >>>>> completely specified state transition/tape operation table. > > "a 100% completely specified state transition/tape operation table" > of a non-existent machine. ========== REMAINDER OF ARTICLE TRUNCATED ==========