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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 25, 2005 5:57 PM

In comp.theory Randy <joe@burgershack.com> wrote:
> stephen@nomail.com wrote:
>> In comp.theory Michael Hennebry <hennebry@web.cs.ndsu.nodak.edu> wrote:
>>

>>>An NP-hard decision problem need not be in NP, but it must be
>>>decidable.

>>
>>
>> I am not sure what the consensus on that is. According
>> to some definitions I have seen the Halting Problem is NP-hard.
>> If you could solve the Halting Problem in polynomial time,
>> you could solve any problem in NP in polynomial time.

> 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.

> For example, a UTM that uses a small number of states will have a lower
> time complexity than a UTM using (or that must explore) a larger number
> of states.

That seems backwards for UTM. In general the number of states a TM
has will have nothing to do with the complexity of its running
time. I really doubt UTM's are an exception.

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
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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
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10/28/05 Bryan Olson
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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