Re: What is the Result from Invoking this Halt Function?

From: George Greene (greeneg_at_greeneg-cs.cs.unc.edu)
Date: 08/13/04 

Date: 13 Aug 2004 13:26:09 -0400

"Peter Olcott" <olcott@worldnet.att.net> writes:
 : Halting Problem according to Alan Turing:
 : The problem of finding out whether a given number is the D.N of a
 : circle-free machine,
 :
 : Translation: (The problem of finding out whether a given Turing Machine
 : Description specifies a Turing Machine that fails to Halt).

These are BOTH wrong. The vast majority of TMs halt ON SOME INPUTS and
loop ON SOME OTHERS. A description of the machine alone WILL NOT answer this
question! You have to describe the machine AND SOME INPUT.
Since the input string is usually presumed finite, you can
without-loss-of-generality specialize to the case where the input has
been included in the machine description and the original input tape is
therefore presumed to be empty, but that complicates the proof.

In any case, the original proof is irrelevant.
What is relevant is that the original proof is ABOUT TURING MACHINES,
and about whether THEY halt or THEY can determine halting. It is not
about whether something with caller-ID can determine halting. 

-- 
 --- The history of our nation has demonstrated that separate is seldom, if ever, equal.
 --- (Feb.3,2004) Supreme Judicial Court of Massachusetts (4-3), adv.Sen.#2175

Relevant Pages