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From: hall@aplcenmp.apl.jhu.edu (Marty Hall)
Subject: Re: "AI Complete" vs the Root Analysis
Message-ID: <DDrrMF.2rM@aplcenmp.apl.jhu.edu>
Organization: JHU/APL AI Lab, Hopkins P/T CS Faculty
References: <41d64d$ped@Mars.mcs.com> <MIKEW.95Aug22151617@hobbes.cs.washington.edu> <DDrDuz.8zt@aisb.ed.ac.uk>
Date: Wed, 23 Aug 1995 15:13:27 GMT
Lines: 24

In article <DDrDuz.8zt@aisb.ed.ac.uk> andrewt@aisb.ed.ac.uk (Andrew Tuson) writes:

>I hate to admit that I`m unsure of the difference between NP-complete and
>NP-hard myself...:-(

Class NP are problems whose solutions can be verified in polynomial
time (or, equivalently, whose solutions can be found in polynomial
time in a NONdeterministic TM).

NP-Complete problems are ones that:
(A) Belong to NP
(B) Are at least as hard as all problems in NP. Ie all NP problems are
    polynomially reducible to it, so that if you could solve it in
    polynomial time, you could solve all NP problems in polynomial
    time (ie P=NP).
Nobody has ever found a polynomial-time algorithm for an NP-Complete
problem, but it has not been proven that one does not exist. 

NP-Hard problems are ones that satisfy (B) but not necessarily (A). Ie
they include all NP-Complete problems as well as for instance problems
that are *proven* to only have exponential-time solutions.

					- Marty
(proclaim '(inline skates))
