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

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Willem

Posts: 145
Registered: 12/10/04
Re: On NP Completeness and Intractability
Posted: Nov 1, 2005 5:02 AM
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Robert wrote:
) For each real number x, consider the decision problem D(x) defined as follows:
)
) Given rational number r, decide whether r < x.

Some would say that that is not a valid definition of a decision problem,
because you are only speculating about its existence, and not actually
describing any single decision problem. This probably boils down to the
axiom of choice in some way.

I think such a decision problem D(x) is decidable iff it can be described.

In any case, the more interesting question is how many *describable*
decision problems are decidable ? You can't hope to solve a problem
if you can't even specify it, after all.

) Note that if an algorithm to solve D(x) exists, x must be constructive in a
) rather strong sense: in particular, the sequence of decimal digits of x is
) recursive. There are of course only countably many such x.

I'm not sure what you mean by 'the sequence is recursive'. Does this
include PI, for example ?


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT


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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