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<H1>NP</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
The class of problems for which answers can be checked for correctness by an algorithm whose run time is  <a href="polynomialtm.html" tppabs="http://hissa.nist.gov/dads/HTML/polynomialtm.html"><em>polynomial</em></a> in the size of the input.  Note that this doesn't require or imply that an answer can be found quickly, only that any claimed answer can be verified or refuted quickly.  "NP" is the class which a <strong>N</strong>ondeterministic machine accepts in <strong>P</strong>olynomial time.
<P><strong>See also</strong>
<a href="npcomplete.html" tppabs="http://hissa.nist.gov/dads/HTML/npcomplete.html"><em>NP-complete</em></a>, <a href="nphard.html" tppabs="http://hissa.nist.gov/dads/HTML/nphard.html"><em>NP-hard</em></a>, <a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>big-O notation</em></a>, <a href="polynmltmalg.html" tppabs="http://hissa.nist.gov/dads/HTML/polynmltmalg.html"><em>polynomial-time algorithm</em></a>.
<P><em>Note:
For instance, a purported <a href="hamilcyc.html" tppabs="http://hissa.nist.gov/dads/HTML/hamilcyc.html"><em>Hamiltonian cycle</em></a> or tour of a <a href="graph.html" tppabs="http://hissa.nist.gov/dads/HTML/graph.html"><em>graph</em></a> can be quickly checked that it, indeed, starts and ends at the same <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertex</em></a>, only uses valid <a href="edge.html" tppabs="http://hissa.nist.gov/dads/HTML/edge.html"><em>edges</em></a>, and visits every other <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertex</em></a> exactly once.  Another example is that a purported sorting of an input can be verified in <a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>O(n<sup>2</sup>)</em></a>. This can be done by sorting the input (again), then comparing it with the purported sorting.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>More information</H2>
History, definitions, examples, etc. given in <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.html">Comp.Theory FAQ</A>, scroll down to <strong>P vs. NP</strong>.

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Entry modified Tue Jul 13 13:03:18 1999.<BR>
HTML page formatted Wed Dec 22 09:35:58 1999.

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