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

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KP Bhat

Posts: 1
Registered: 10/25/05
Re: On NP Completeness and Intractability
Posted: Oct 25, 2005 6:06 PM
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martin dowd wrote:
> Important examples of unsolvable problems include:
> -is a statement of predicate logic valid?
> -is a statement in the language of rings true in the theory of rings?
> -is a polynomial with integer coefficients have an integer root?
> The list goes on.
>
> NP hard means every problem is NP is no harder. NP complete means in
> addition the problem is in NP.
>


My $0.02 worth...

The meaning of the word "hard" refers to time complexity. In order to
be NP-Hard, the time complexity should be worse than or equal to the
time complexity of a known problem in NP. It's as if we are saying
"As bad as NP". Furthermore, even though we make that comparison,
the problem itself may not even be in NP. We are using NP as just the
benchmark. That is why unsolvable problems like the Halting Problem
are considered NP-Hard (all we are saying is that it is as bad as any
NP problem out there). When a problem is NP-Hard and it itself is in
NP, then it is called NP-Complete.

Cook (the gentleman who opened this whole can of worms in 1971)
conjectured something to this effect:

"If the satisfiability problem can be solved in polynomial time, a
non-deterministic Turing Machine will be no more powerful than a
deterministic Turning machine. In other words, non-determinism alone
will not help in solving any problem".

In course of time, people reduced other problems to the satisfiability
problem (i.e the set of NP Complete problems expanded rapidly),
effectively saying that if a polynomial algorithm can be found for any
one of these problems, then P=NP. By the same token, if it can be
proven that no polynomial algorithm for any one of these problems, P !=
NP




Having said that, can someone come up with more problems that are
NP-Hard ---- BUT NOT ------ NP Complete? Dowd's list above is a good
starting point. My guess is that only a handful of problems fall into
this category.

Is that correct?

IMHO an overwhelming majority of NP-Hard problems are also NP-Complete.


Thanks,
Bhat



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

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