Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory,sci.logic Subject: Re: A computable function that reports on the behavior of its actual self is not allowed Date: Sun, 12 May 2024 18:19:12 -0500 Organization: A noiseless patient Spider Lines: 106 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 13 May 2024 01:19:13 +0200 (CEST) Injection-Info: dont-email.me; posting-host="822a7b45c10435b9354ed3bfb60d5b64"; logging-data="3202321"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19VuHfZboHJQA/Bcq6bN/ns" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:buZ1yIifsxGfGfrBiG7OcYgGQMc= In-Reply-To: Content-Language: en-US Bytes: 5751 On 5/12/2024 5:40 PM, Richard Damon wrote: > On 5/12/24 6:21 PM, olcott wrote: >> On 5/12/2024 4:40 PM, Richard Damon wrote: >>> On 5/12/24 5:18 PM, olcott wrote: >>>> On 5/12/2024 2:27 PM, olcott wrote: >>>>> Computable functions are the basic objects of study in computability >>>>> theory. Computable functions are the formalized analogue of the >>>>> intuitive notion of algorithms, in the sense that a function is >>>>> computable if there exists an algorithm that can do the job of the >>>>> function, i.e. given an input of the function domain it can return the >>>>> corresponding output. >>>>> https://en.wikipedia.org/wiki/Computable_function >>>>> >>>>> A computable function that reports on the behavior of its actual >>>>> self (or reports on the behavior of its caller) is not allowed. >>>>> >>>>> A decider must halt whereas simulating a pathological input >>>>> that would never halt unless aborted can only halt by aborting. >>>>> >>>>> This causes the direct execution of this input after it has been >>>>> aborted >>>>> to have different behavior than the simulated input that cannot >>>>> possibly >>>>> stop running unless aborted. >>>>> >>>> >>>> *MORE PRECISE WORDING* (this may take a few more rewrites) >>>> When Ĥ is applied to ⟨Ĥ⟩ >>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >>>> >>>> It is a verified fact that the directly executed Ĥ ⟨Ĥ⟩ cannot possibly >>>> stop running unless simulating partial halt decider embedded_H aborts >>>> its simulation of its input. >>> >>> But since embedded_H implements a specific algorithm, either it will >>> or it won't. "unless" is a meaningless word here, it implies a case >>> that can't happen. >>> >>> We can look at the two possible cases. >>> >>> First, if embedded_H doesn't ever abort its simulation, then, as you >>> have desceribed, THAT embedded_H creates a H^ that will never halt, >>> but the H that was based on will also never abort its simulation (or >>> you lied that embedded_H is the needed copy of H) and thus never >>> answer and fail to be a decider. >>> >> >> It can answer without halting by transitioning to its own internal >> non-final state of embedded_H.qn without ever reaching Ĥ.qn. Every >> simulated instance of embedded_H would do this same thing and then >> continue simulating its input. > So, you just don't understand how algorithms work, and how compuations > are DEFINED. > > > If you want to try to define a new system of compuation that allows > giving answer without the algorithm ending, but still allows all the > composition operations that are included in computation theory, go ahead > and try. > > You then need to show that it is Turing Complete, which means that you > can't outlaw any computation allowed in a Turing Machine, like H^. > >> >> In this case embedded_H an actual UTM that has the extra >> feature of examining all of the state transitions of its input >> to see what we can all see that Ĥ ⟨Ĥ⟩ remains stuck in recursive >> simulation. >> > > And a UTM doesn't reveal its answer until it come to a final state, just > like ALL Turing Machines or equivalent computation. > >> *Or we can get an actual partial halt decider as follows* >> *Or we can get an actual partial halt decider as follows* >> *Or we can get an actual partial halt decider as follows* >> >> No decider is ever allowed to report on its own behavior thus embedded_H >> as a simulating partial halt decider is NOT ALLOWED to report on the >> direct execution of Ĥ ⟨Ĥ⟩ because this IS REPORTING ON ITS OWN BEHAVIOR. > > WHO SAYS THIS? A decider must compute the mapping from an input. Its actual self cannot possibly be an input. No decider takes an actual Turing machine as input thus no decider can possibly take its actual self as input. (a) The behavior of the directly executed Ĥ ⟨Ĥ⟩ is after embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ has already aborted its simulation. (b) The behavior of the simulated input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ is before embedded_H has aborted its simulation. (c) These two behaviors (a) and (b) ARE NOT THE SAME. (a) will stop running on its own (b) will never stop running unless aborted. *THIS MAKES THE BEHAVIOR OF THE DIRECT EXECUTION* *AN INCORRECT MEASURE FOR PATHOLOGICAL INPUTS* -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer