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Topic: On NP Completeness and Intractability
Replies: 90   Last Post: Nov 1, 2005 8:08 PM

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 stephen@nomail.com Posts: 1,744 Registered: 12/13/04
Re: On NP Completeness and Intractability
Posted: Oct 26, 2005 2:49 PM

In comp.theory Randy <joe@burgershack.com> wrote:
> stephen@nomail.com wrote:
>> In comp.theory Randy <joe@burgershack.com> wrote:
> ...
>>>I think any algorithm that contains uncertainty (indefinite input) can
>>>still be assessed for time or space complexity. Whenever the problem
>>>cannot be solved, its complexity must remain undefined. However, it
>>>seems to me that when the problem can be solved, its complexity can be
>>>characterized and maybe quantified.

>>
>>
>> Noone was talking about indefinite input. The Halting Problem
>> is unsolvable and there is nothing indefinite or uncertain about
>> the input.

> The halting problem is entirely about what is known about: 1) the
> program's input or 2) the program's search space. If there is no input,
> or the input is completely known, or the search space is completely
> known, then the program is deterministic and can be guaranteed to halt.

No. You are totally wrong. A deterministic algorithm is
not guaranteed to halt.

> Halting is only undecidable when the input that is incompletely known
> (e.g. infinite), or has an incompletely known effect on the program, as
> in external instruction streams that might include or induce infinite
> loops. Halting is also undecidable when the program's search space may
> not include solutions that satisfy the program's given constraints and
> is infinite, potentially causing the search to continue forever.

This is just nonsense. The halting problem is defined as follows:
Given a program x and an input y, does x halt on y?
x and y are both finite. There does not exist an algorithm
that when given an x and y, always produces the correct
answer. That is what it means for the problem to be unsolvable.

> Not being a mathematician, I can only guess that at its essence,

Stephen

Date Subject Author
10/25/05 nimmi_srivastav@yahoo.com
10/25/05 Dr. David Kirkby
10/25/05 ianparker2@gmail.com
10/25/05 Pubkeybreaker
10/25/05 osmium
10/25/05 Pubkeybreaker
10/25/05 Willem
10/25/05 Bryan Olson
10/25/05 Willem
10/25/05 Ed Prochak
10/25/05 Dr. David Kirkby
10/25/05 Gene
10/25/05 MartDowd
10/25/05 RobertSzefler
10/25/05 Dr. David Kirkby
10/25/05 Pubkeybreaker
10/25/05 Wim Benthem
10/26/05 RobertSzefler
10/25/05 KP Bhat
10/25/05 stephen@nomail.com
10/25/05 tchow@lsa.umich.edu
10/25/05 googmeister@gmail.com
10/25/05 nimmi_srivastav@yahoo.com
10/25/05 stephen@nomail.com
10/26/05 tchow@lsa.umich.edu
10/27/05 stephen@nomail.com
10/25/05 stephen@nomail.com
10/25/05 Randy
10/25/05 C6L1V@shaw.ca
10/25/05 stephen@nomail.com
10/25/05 Wim Benthem
10/25/05 stephen@nomail.com
10/25/05 Randy
10/25/05 stephen@nomail.com
10/26/05 tchow@lsa.umich.edu
10/26/05 Randy
10/27/05 Arthur J. O'Dwyer
10/27/05 Randy
10/27/05 Willem
10/27/05 Randy
10/27/05 stephen@nomail.com
10/27/05 Randy
10/27/05 stephen@nomail.com
10/27/05 Randy
10/27/05 stephen@nomail.com
10/27/05 tchow@lsa.umich.edu
10/27/05 Randy
10/27/05 tchow@lsa.umich.edu
10/27/05 Joe Hendrix
10/27/05 Randy
10/27/05 Joe Hendrix
10/27/05 Randy
10/27/05 stephen@nomail.com
10/27/05 Arthur J. O'Dwyer
10/27/05 googmeister@gmail.com
10/27/05 tchow@lsa.umich.edu
10/27/05 Randy
10/27/05 Arthur J. O'Dwyer
10/28/05 Joe Hendrix
10/28/05 Ben Rudiak-Gould
10/28/05 Bryan Olson
10/28/05 Pekka Orponen
10/27/05 tchow@lsa.umich.edu
10/27/05 Randy
10/25/05 tchow@lsa.umich.edu
10/25/05 Michael J. Hennebry
10/25/05 stephen@nomail.com
10/25/05 Randy
10/25/05 stephen@nomail.com
10/25/05 Willem
10/25/05 Arthur J. O'Dwyer
10/25/05 googmeister@gmail.com
10/31/05 Oliver Wong
10/31/05 Robert Israel
11/1/05 Willem
11/1/05 googmeister@gmail.com
11/1/05 Willem
11/1/05 Torkel Franzen
11/1/05 googmeister@gmail.com
11/1/05 Oliver Wong
11/1/05 Willem
11/1/05 Robert Israel
10/26/05 Randy
10/26/05 stephen@nomail.com
10/26/05 Randy
10/27/05 Bryan Olson
10/27/05 Randy
10/27/05 Bryan Olson
10/27/05 Randy
10/25/05 Pat Farrell
10/25/05 Bryan Olson