Re: Alan Turing's Halting Problem is incorrectly formed (PART-TWO)

From: Daryl McCullough (daryl_at_atc-nycorp.com)
Date: 06/23/04 

Date: 23 Jun 2004 07:20:59 -0700

David C. Ullrich says...

>>> Peter Olcott says...

>>> >function LoopIfHalts (M, w):
>>> > if WillHalt (M, w) then
>>> > while true do {}
>>> > else
>>> > return false;

>There's more than one question here. What you just
>said _is_ the correct answer to the question of what
>LoopHalts() does. It follows from that that WillHalt
>is not giving correct answers about whether or not
>an arbitrary program halts.

Actually, Peter screwed up the counterexample. If you
are asking "Does LoopIfHalts halt?" you need to specify
the inputs. It has two input parameters, M and w. What
is Peter wanting M and w to be? Presumably, he wants
M to be the code for LoopIfHalts. But then what's w?

I think what he meant to write was something more like:

   function LoopIfHalts(M):
      if WillHalt (M, M) then
          while true do {}
      else
          return false;

Then he would like to ask "Does LoopIfHalts halt when
given (the code for) LoopIfHalts as an input?" 

--
Daryl McCullough
Ithaca, NY

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