Re: [PO] Proving a negative is hard
From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 08/24/04
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Date: Tue, 24 Aug 2004 10:06:07 +0200
Peter Olcott wrote:
> "Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message news:2os9u5Fdrl1eU1@uni-berlin.de...
>>Peter Olcott <olcott@worldnet.att.net> wrote:
>>>"Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message
>>>
>>>>Every transition in a TM writes something to the tape. It
>>>
>>>I don't yet accept that this is true. It certainly does not
>>>seem to be required. This seems like a false assumption.
>>
>>I don't think you get it. This is just how TMs are defined.
>
> Not according to another respondent's direct quote of Turing.
> Turing said it more towards the way that I am saying it.
1) section 7 of Turing's paper explains it better (as
someone here pointed out.
2) I find Turing difficult to follow because I'm used to the
language given in Davis "Computability and Unsolvability"
and Hopcroft&Ullman "Intro to Automata..." (two slightly
different ways of expresing the same thing as Turing
3) I think the other respondent quoted an irrelevant
selection.
Maybe you should consult another source. Only having seen
the few pages of your text (Linz) you scanned, I think your
reading of that is problematic.
...
>>Are you implying that there is another definition of function other than
>>the mathematical one?
>
> Math functions must always return a result.
> C++ void functions never return a result.
> My method provides the means to selectively refrain
> from returning a result.
Your way of labeling things leads me to believe that we have
quite different world views. We're not just talking past
each other. We're talking in separate "cones of silence".
OK. Suppose we give (or take commonly accepted versions of)
mathematical definitions of "math function" and "C++ void
function". These definitions must operate -mathematically-,
logically, that's all I'm saying. So we're using the same
word, function, in two different ways. We've all known this
all along, it's just that it finally bugged me enough.
> Given arbitrary restrictions the problem can not be solved within
> the context of these arbitrary restrictions. Remove the arbitrary
> restrictions, and you have more options available.
There you have no argument from me.
It's just that the "arbitrary" restrictions/definitions for
TMs happen to define a model of computation that is
surprisingly equivalent in power (computability) to whole
bunch of other independently designed computation models,
which are all very reasonable (lambda calculus, term rewrite
systems, poly eqns over integers, two-stack machines
(pushdown automata with 2 stacks), tiling systems, register
machines (close to conventional computer operation), etc, etc.
If you can find the analogous concept of "-always- returning
a result" in all these other computing models (that would be
interesting in and of itself), and show that these analogous
properties are also poorly motivated (as you claim it is for
TMs), then maybe you might convince more people of the
relevance of your methods.
-- Mitch Harris (remove q to reply)
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