Path: ...!weretis.net!feeder9.news.weretis.net!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: Tue, 28 May 2024 07:34:21 -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 11:34:22 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2469061"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 9740 Lines: 206 On 5/27/24 11:24 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. >> > > *Not exactly, you are misreading this* > > The domain of this problem is to be taken as the set of all Turing > machines and all w; that is, we are looking for a single Turing machine > that, given the description of an arbitrary M and w, will predict > whether or not the computation of M applied to w will halt *** a single Turing Machine *** not singular > > ... > > Proof: We assume the contrary, namely that there exists an algorithm, > and consequently some Turing machine H, that solves the halting problem > https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf *** some Turing Machine *** Note singular > > Ordinary existential quantification looks for at least one > element not exactly one element: But you can look for at least one by looking for one without an assumption that it is unique. ========== REMAINDER OF ARTICLE TRUNCATED ==========