Re: Generation of permutations

[Stephen Leake <stephen.a.leake.1@gsfc.nasa.gov>]

"Chad R. Meiners" <crmeiners@hotmail.com> writes:

> No that is not what Robert was saying.  He was referring to Rice's Theorem
> for which you can clearly show that the problem of determining whether a
> given set of machine instructions will sort an given input is
> Turing-undecidable.  How did you come to such a misinterpretation?

Doesn't sound like a "misinterpretation" to me.

Let's try some symbolic logic:

A : "a given set of machine instructions"
B : "a given input"
C : A sorts B

Rice's Theorem says statement C is "Turing-undecideable". 

Question; does that mean C is "false"?

A' : "set of instructions emitted by GNAT for bubble sort"
B' : "a given input"
C' : A' sorts B'

So Rice's Theorem says statement C' is "Turing-undecideable".  

Is C' "true"?

If C' is "true", does that mean A' "constitutes a general sorting
algorithm". I think so, if we assume B' is allowed to vary over all
possible inputs.

I suspect the problem here lies in the conflict between the English
meanings of "true" and "decideable", and the formal meaning of
"Turing-(un)decideable". We all believe that C' is "true", but that's
not the same as "Turing-decideable".

I'll leave it to someone else to give the formal definition of
"Turing-decideable"; I'm sure I'd get it wrong :).

> 
> 
> <tmoran@acm.org> wrote in message
> news:p_iB8.3409$9d1.36389081@newssvr21.news.prodigy.com... > > but
> to determine whether a set of instructions constitutes a general > >
> sorting algorithm is obviously recursively undecidable. > So the set
> of instructions emitted by Gnat when it compiles bubble sort > code
> may or may not constitute a general sorting algorithm, and whether >
> it does or not is undecidable? I learn something new every day.
> 
> 

-- 
-- Stephe