Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Simulation vs. Execution in the Halting Problem Date: Mon, 2 Jun 2025 10:23:15 -0500 Organization: A noiseless patient Spider Lines: 82 Message-ID: <101kfl3$3bfvj$4@dont-email.me> References: <101a7uv$3vfam$5@dont-email.me> <101br7m$db03$1@dont-email.me> <101cjk7$hfof$7@dont-email.me> <101hdjt$21ui2$1@dont-email.me> <101iheg$2h3fr$1@dont-email.me> <101jhvm$33lln$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 02 Jun 2025 17:23:16 +0200 (CEST) Injection-Info: dont-email.me; posting-host="01672d8ae9aa1e0fec727857b1cb5419"; logging-data="3522547"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX195QzKWFwavhI02oAfJfI9M" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:fywktGMDHzJSWtnZvmK+3ZB0uDo= X-Antivirus: Norton (VPS 250602-4, 6/2/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US In-Reply-To: <101jhvm$33lln$1@dont-email.me> Bytes: 4069 On 6/2/2025 1:56 AM, Mikko wrote: > On 2025-06-01 21:41:36 +0000, olcott said: > >> On 6/1/2025 6:30 AM, Mikko wrote: >>> On 2025-05-30 15:41:59 +0000, olcott said: >>> >>>> On 5/30/2025 3:45 AM, Mikko wrote: >>>>> On 2025-05-29 18:10:39 +0000, olcott said: >>>>> >>>>>> On 5/29/2025 12:34 PM, Mr Flibble wrote: >>>>>>> >>>>>>> 🧠 Simulation vs. Execution in the Halting Problem >>>>>>> >>>>>>> In the classical framework of computation theory (Turing machines), >>>>>>> simulation is not equivalent to execution, though they can >>>>>>> approximate one >>>>>>> another. >>>>>> >>>>>> To the best of my knowledge a simulated input >>>>>> always has the exact same behavior as the directly >>>>>> executed input unless this simulated input calls >>>>>> its own simulator. >>>>> >>>>> The simulation of the behaviour should be equivalent to the real >>>>> behaviour. >>>> >>>> That is the same as saying a function with infinite >>>> recursion must have the same behavior as a function >>>> without infinite recursion. >>> >>> A function does not have a behaviour. A function has a value for >>> every argument in its domain. >>> >>> A function is not recursive. A definition of a function can be >>> recursive. There may be another way to define the same function >>> without recursion. >>> >>> A definition of a function may use infinite recursion if it is also >>> defined how that infinite recursion defines a value. >>> >>> Anyway, from the meaning of "simulation" follows that a simulation >>> of a behaviour is (at least in some sense) similar to the real >>> behaviour. Otherwise no simulation has happened. >>> >> >> void DDD() >> { >>    HHH(DDD); >>    return; >> } >> >> The *input* to simulating termination analyzer HHH(DDD) >> specifies recursive simulation that can never reach its >> *simulated "return" instruction final halt state* > > It does not matter whether a particular simulation does or does not > reach its "return" instruction. It completely matters. DDD correctly simulated by HHH proves the exact behavior that the input to HHH(DDD) actually specifies. > It only matters whether whether the > beahaviour specified by the input (which in this case is DDD) will > reach its own "return", and it does. > The behavior specified by the input never reaches its own "return" instruction. You are confusing the behavior specified by the input with the behavior of its caller. int main() { DDD(); // calls HHH(DDD) that cannot report on the behavior } // of its caller because its caller is *not* its input. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer