A Possible "solution" to the Halting Problem
in [Theory]
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From: Peter Olcott on 20 Oct 2006 16:24 "Jack Campin - bogus address" <bogus(a)purr.demon.co.uk> wrote in message news:bogus-6F2222.11112720102006(a)news.news.demon.net... > "Peter Olcott" <NoSpam(a)SeeScreen.com> wrote: >> if (MalignantSelfReference(SourceCode, InputData)) > > This isn't code, it's wishful thinking. You haven't proved that > any such function as MalignantSelfReference can exist, you haven't > programmed it, and you haven't proved that it always returns a value. > > For that matter you haven't even *specified* it. I have specified it several times, you are merely looking at it through the biased filter of a closed mind. > > ============== j-c ====== @ ====== purr . demon . co . uk ============== > Jack Campin: 11 Third St, Newtongrange EH22 4PU, Scotland | tel 0131 660 4760 > <http://www.purr.demon.co.uk/jack/> for CD-ROMs and free | fax 0870 0554 975 > stuff: Scottish music, food intolerance, & Mac logic fonts | mob 07800 739 557
From: Peter Olcott on 20 Oct 2006 16:28 "Aatu Koskensilta" <aatu.koskensilta(a)xortec.fi> wrote in message news:VF1_g.9762$aa.9293(a)reader1.news.jippii.net... > Jack Campin - bogus address wrote: >> "Peter Olcott" <NoSpam(a)SeeScreen.com> wrote: >>> if (MalignantSelfReference(SourceCode, InputData)) >> >> This isn't code, it's wishful thinking. You haven't proved that >> any such function as MalignantSelfReference can exist, you haven't >> programmed it, and you haven't proved that it always returns a value. >> >> For that matter you haven't even *specified* it. > > He has said something to the effect that a program contains "malignant > self-reference" if it has a call to Halt with its own source as an argument. AND, the return value of this call to Halt() is specifically and intentionally used to corrupt this result. There are other required factors too, essentially if it is in the form of the provided example then it is the form of MALIGNANT_SELF_REFERENCE. > > -- > Aatu Koskensilta (aatu.koskensilta(a)xortec.fi) > > "Wovon man nicht sprechen kann, daruber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Peter Olcott on 20 Oct 2006 16:31 "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message news:ehab9n01r9b(a)drn.newsguy.com... > Aatu Koskensilta says... >> >>Jack Campin - bogus address wrote: >>> "Peter Olcott" <NoSpam(a)SeeScreen.com> wrote: >>>> if (MalignantSelfReference(SourceCode, InputData)) >>> >>> This isn't code, it's wishful thinking. You haven't proved that >>> any such function as MalignantSelfReference can exist, you haven't >>> programmed it, and you haven't proved that it always returns a value. >>> >>> For that matter you haven't even *specified* it. >> >>He has said something to the effect that a program contains "malignant >>self-reference" if it has a call to Halt with its own source as an argument. > > I seem to remember an article from long ago in which Peter suggested > that tight computer security could be used to solve the halting > problem. The idea is that you keep the source code for Halt secret, > so that nobody can ever use it to generate a logical contradiction. > > -- > Daryl McCullough > Ithaca, NY > That entire line-or-reasoning had been correctly refuted by a PhD computer science professor calling themselves NewToMe. The line-of-reasoning that I am providing now is the only possible line-of-reasoning that could work within the categorically complete enumeration of every possible line-of-reasoning that could ever possibly exist.
From: Patricia Shanahan on 20 Oct 2006 16:53 Peter Olcott wrote: > "Ben Bacarisse" <ben.usenet(a)bsb.me.uk> wrote in message > news:87y7rbmum0.fsf(a)bsb.me.uk... >> "Peter Olcott" <NoSpam(a)SeeScreen.com> writes: >> >>> It is equivalent to saying that no correct answer exists to the >>> question, "How tall are you green or blue?" because the question >>> itself is ill-formed. It is not at all equivalent to I_GIVE_UP. >> You have not been able to say exactly when a question is ill-formed, > > I have said this many times here it is again. > > // > // To make the problem more clear we are assuming > // that function call syntax results in inline expansion, > // thus specifying the name of a function specifies the > // text body of the function. > // > > void LoopIfHalts(string SourceCode) { > if ( WillHalt(SourceCode, SourceCode) == TRUE ) > while (TRUE) // loop forever > ; > else > return; > } > > int WillHalt(string SourceCode, string InputData) { > if (MalignantSelfReference(SourceCode, InputData)) > throw(MALIGNANT_SELF_REFERENCE); > if ( TheProgramWillHalt(SourceCode, InputData) ) > return TRUE; > else > return FALSE; > } > > LoopIfHalts(LoopIfHalts); > > // ANALYTICAL COMMENTARY > WillHalt() is provided with the source code of LoopIfHalts(), as > input, so WillHalt() can see exactly how the return value of the > invocation of itself under test will be used to toggle the result > of the analysis of the invocation of itself under test. WillHalt() > can see that LoopIfHalts() is toggling the result of the invocation > of itself under test to invalidate the analysis of the invocation > of itself under test. > > Therefore WillHalt() can determine that the question: > "Does LoopIfHalts(LoopIfHalts) halt?" has no correct YES or NO > answer, and is thus erroneously formed because it is asking a > YES or NO question that has no correct YES or NO answer. > > In order to define a function you need to state the domain and co-domain, and a rule determining which element of the co-domain is associated with each element of the domain. All you have told us about MalignantSelfReference is a single element of its domain, and that it is true for that element. From its use in an if-test, I assume it is a Boolean function, a function whose co-domain is a set containing some representation of "true" and "false", but I have not yet been told about any element of its domain for which it is false. If its domain really only contained one element, then it could be defined by telling us the value for that element. However, that would make it inappropriate for the way it is being used in WillHalt. Without a definition, other than a single domain-range pair, for MalignantSelfReference, the source code is useless for defining your WillHalt. Patricia
From: Peter Olcott on 20 Oct 2006 16:54
"Patricia Shanahan" <pats(a)acm.org> wrote in message news:4J3_g.9838$Lv3.8958(a)newsread1.news.pas.earthlink.net... > Peter Olcott wrote: >> "Patricia Shanahan" <pats(a)acm.org> wrote in message > ... >> I will only proceed beyond this example, iff you agree that I have made my >> point with this example. > > Bye. I would much rather fail to make my point entirely that to get caught up in any endlessly circular arguments. I simply don't have time for these. If the only way that you can possibly refute me is by continuing to change the subject, then you have not refuted me at all. Try it with the more specific break down. You as a human can see the greater perspective regarding whether or not LoopIfHalts(LoopIfHalts) will halt. You can see that it will halt, the correct asnwer is obviously YES. Let's take this next step: What correct YES or NO answer can WillHalt() provide to LoopIfHalts() ??? Are you seeing something that WillHalt() can not possibly see, or are you merely providing an answer that WillHalt() can not possibly provide? Is there any difference what-so-ever between KNOWING an answer, and PROVIDING an answer? Is KNOWING an answer 100% exactly and precisely the same thing as PROVIDING and answer? |