Path: 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: Sun, 8 Jun 2025 01:00:50 -0500 Organization: A noiseless patient Spider Lines: 106 Message-ID: <10238ui$3m1s3$2@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> <101kfl3$3bfvj$4@dont-email.me> <101m9ps$3srp4$1@dont-email.me> <101nltk$7qau$10@dont-email.me> <101osq3$mlio$1@dont-email.me> <101ps65$ta6v$8@dont-email.me> <102388o$3m38c$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 08 Jun 2025 08:00:50 +0200 (CEST) Injection-Info: dont-email.me; posting-host="a9517e45c46a9e6e81edd5eee2519f49"; logging-data="3868547"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/0hNSWFg2FciPysGB7myE6" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ih1IFX3yNr3Esc43AnT9wPkOGjY= Content-Language: en-US In-Reply-To: <102388o$3m38c$1@dont-email.me> X-Antivirus: Norton (VPS 250608-0, 6/7/2025), Outbound message X-Antivirus-Status: Clean On 6/8/2025 12:49 AM, Mikko wrote: > On 2025-06-04 16:27:48 +0000, olcott said: > >> On 6/4/2025 2:32 AM, Mikko wrote: >>> On 2025-06-03 20:28:36 +0000, olcott said: >>> >>>> On 6/3/2025 2:55 AM, Mikko wrote: >>>>> On 2025-06-02 15:23:15 +0000, olcott said: >>>>> >>>>>> 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 proves nothing without a proof that DDD is correctly simulated >>>>> by HHH. >>>> >>>> I have shown that proof too many times and people >>>> denied the very obvious verified facts of it. >>> >>> You have never shown any proof of anything. But a verifiable and >>> verified >>> fact is that DDD halts. An obvious conseqence of that fact is that every >>> report that means 'DDD does not halt' is wrong. >> >> When I provide proof that you cannot understand >> this does not mean that I did not provide proof. > > Yes, it does. What I just said is a truism, tautology, self-evident truth. In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof... https://en.wikipedia.org/wiki/Self-evidence > To understand a proof does not require any skills other > than proof checking, which is a Turing computable function. > -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer