Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: comp.theory Subject: Re: Defining a correct halt decider Date: Tue, 3 Sep 2024 18:53:18 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Tue, 3 Sep 2024 18:53:18 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="739540"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 3542 Lines: 55 Am Tue, 03 Sep 2024 08:17:56 -0500 schrieb olcott: > On 9/3/2024 3:44 AM, Mikko wrote: >> On 2024-09-02 16:06:11 +0000, olcott said: >> >>> A correct halt decider is a Turing machine T with one accept state and >>> one reject state such that: >>> If T is executed with initial tape contents equal to an encoding of >>> Turing machine X and its initial tape contents Y, and execution of a >>> real machine X with initial tape contents Y eventually halts, the >>> execution of T eventually ends up in the accept state and then stops. >>> If T is executed with initial tape contents equal to an encoding of >>> Turing machine X and its initial tape contents Y, and execution of a >>> real machine X with initial tape contents Y does not eventually halt, >>> the execution of T eventually ends up in the reject state and then >>> stops. >> Your "definition" fails to specify "encoding". There is no standard >> encoding of Turing machines and tape contents. >> > That is why I made the isomorphic x86utm system. > By failing to have such a concrete system all kinds of false assumptions > cannot be refuted. What would those assumptions be? > The behavior of DDD emulated by HHH** different than the behavior > of the directly executed DDD** **according to the semantics of the x86 > language How can the same code have different semantics? > HHH is required to report on the behavior tat its finite string input > specifies even when this requires HHH to emulate itself emulating DDD. The input specifies an aborting HHH - which you don’t simulate. > DDD never halts unless it reaches its own final halt state. The fact > that the executed HHH halts has nothing to do with this. Other than that DDD calls HHH? > HHH is not allowed to report on the computation that itself is contained > within. Then it is only partial, and doesn’t even solve the case it was built for. > Except for the case of pathological self-reference the behavior of the > directly executed machine M is always the same as the correctly > simulated finite string ⟨M⟩. That sure sounds like a mistake to me. > That no one has noticed that they can differ does not create an axiom > where they are not allowed to differ. They were never allowed, that was the definition. > No one noticed that they differ only because everyone rejected the idea > of a simulating halt decider out-of-hand without review. I think after 3 years that excuse has grown a bit stale. -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.