Nondeterministic polynomial time
A
verifier
for a language A is an algorith=
m V, where
A =3D {w
| V accepts <w,c> for some string c}.
We
measure the time of a verifier only in terms of the length of w, so a polynomial time verifier runs
in polynomial time in the length of w.
A
language A is polynomially
verifiable if it has a polynomial time verifier.
NP is the class of languages that=
have
polynomial time verifiers.
NTIME(t(n))
=3D {L| L is a language decided by a O(t(n)) time nondeterministic Turing
machine}.
NP =3D ![](3D"03_nondeterministicpolynomialtime_files/image003.gif")
NTIME(nk)
The best method known for solving languages in NP =
deterministically uses
exponential time. (Remember, computers are deterministic by their very natu=
re.)
NP
&Iacu=
te;
EXPTIME =3D ![](3D"03_nondeterministicpolynomialtime_files/image005.gif")
TIME(2![](3D"03_nondeterministicpolynomialtime_files/image007.gif")
)
Exponential
time algorithms typically arise when we solve problems by exhaustively
searching through a space of solutions, called brute-force search.=
Sometimes,
brute-force search may be avoided through a deeper understanding of a probl=
em,
which may reveal a polynomial time algorithm.
The
question of whether P =3D NP is one of the greatest unsolved problems in
theoretical computer science and contemporary
mathematics.
If
these classes were equal, any polynomially veri=
fiable
problem would also be polynomially decidable/solvable.
People
have invested enormous effort to find polynomial time algorithms for certain
problems in NP and have proven unsuccessful.
In
order to prove that the two classes are in fact unequal, one would have to =
show
that no fast algorithm exists to replace brute-force search. Doing so is
currently beyond scientific research.
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image001.jpg
Content-Transfer-Encoding: base64
Content-Type: image/jpeg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------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image002.wmz
Content-Transfer-Encoding: base64
Content-Type: image/x-wmz
H4sIAAAAAAACC7t+9tgsBjBwYF7AxMgJYn2IZ2QAMphPAtlMDDJgWVYg5mSCsZgYGaEsRqb///+D
WXqMElAxbrg6HqYFTA7MQkCWGhs/gxTDf5BiBgEg/wCQtR3EY2ZgCAeq54aq4WHwTSzJCKksSGVg
aADb/ZvpwF+ICyeALGViYWIQ8A1RcK0oKUpk4OSSXPBRiGHHks/lB4FYweBreSpX2nwWoEJdoGoO
IG3E9YNRjwGkNbQSYp7Cf5h5IFGQeSGZuanFCn6p5QpB+bmJeTjMY2QA0R/g5noyrQSbkF3JBXU9
F9iHjGDTIXYJMLCDeXvAYcLIxKQUXFlckprLMB9kLgNQhyJDF0QDSNVnIQaY2yF2MYICCAgAj05n
lKgBAAA=
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image003.gif
Content-Transfer-Encoding: base64
Content-Type: image/gif
R0lGODlhIwAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAU
ABYAgwAAAFtaW3Z2dmppapubm4uKiqmpqby8vLCwsLa2ts3NzcLCwsfHxwECAwECAwECAwRWUIBJ
65RW2Q105l8ITl5Vjic5Umm3qiK6tXP9tnQMr/jr6pzebbMIrAYLksdAWBEMOwHDyAkwMJrlgVoJ
HBCsE4JBGEwGBEbClCogFgrFAlEwuXJBVQQAOw==
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image004.wmz
Content-Transfer-Encoding: base64
Content-Type: image/x-wmz
H4sIAAAAAAACC7t+9tgsBjA4wJTAzMgJYm2IZ2QAMphPAtlMDDJgWVYg5mSCsZgYGaEsRqb///+D
WXqMElAxbrg6HqCZB5iEgCw1Nn4GKYb/IMUMAiDbgKztQNwAVCvODNQDVcPD4JtYkhFSWZDKwPAA
bPdvpgN/IS6cALKUiYWJQcA3RMG1oqQokYGVq2vBRyGGHUs+lx8EYgWDr+UTONI4WIAKdYGqOYC0
EddPRj0GkNbQSoh5Cv9h5oFEQeaFZOamFiv4pZYrBOXnJubhMI+RAUR/gJsrwbwFbG52JRfU9Vxg
HzKCTYfYJcDADubtAYcJIxOTUnBlcUlqLgMHyFwGoA5Fhi6IBpCqz0IMMLdD7GJkYAbLAADbZhFq
qAEAAA==
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image005.gif
Content-Transfer-Encoding: base64
Content-Type: image/gif
R0lGODlhHQAkAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAO
AB8AgwAAAFtaW3Z2dmppapubm4uKiqmpqby8vLCwsLa2ts3NzcLCwsfHxwECAwECAwECAwRTUIBJ
6xTKaqDyrt0HeiJHimFpqquali96fjE9bzW+BOWwGIQSwSBg8DYBhsRwOFYCBwQFwSAMJgMCI2Ep
IBadBaLAKptdN01azUGzcpaMHDW5RQAAOw==
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image006.wmz
Content-Transfer-Encoding: base64
Content-Type: image/x-wmz
H4sIAAAAAAACC7t+9tgsBjB4wMjAxMgJYn2IZWQAMphPAtlMDDJgWVYg5mSCsZgYGaEsRqb///+D
WXqMElAxbrg6HiYGpgeMQkCWGhs/gxTDf5BiBgEg/wCQtR2IFwAN2g7E3FA1PAy+iSUZIZUFqQwM
BmC7fzMp/Ie4cALYVhYmBoGQzNzUYgW/1HKFoPzcxDyGHUs+lx8EYgWDr+VOHGmJLEB1ukDFHEDa
iOsLgzRYZ3YlxLyGf+SZx8gAoj/AzV3AaMUAMiGvkgvqei6wDxnBpkPsEmBgB/P2gMOEkYlJKbiy
uCQ1lyERZC4DUIciQxdEAxDEfBZigLkdYhcjAzNYBgBkfjZVqAEAAA==
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/image007.gif
Content-Transfer-Encoding: base64
Content-Type: image/gif
R0lGODlhFAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAP
AA4AgAAAAM3NzQIfhI8QkW3sGoPx0apunArDD3qdlixPZXboQbJuq2ZVAQA7
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/oledata.mso
Content-Transfer-Encoding: base64
Content-Type: application/x-mso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=
------=_NextPart_01C5FBD5.97BDC790
Content-Location: file:///C:/1A8BB205/03_nondeterministicpolynomialtime_files/filelist.xml
Content-Transfer-Encoding: quoted-printable
Content-Type: text/xml; charset="utf-8"