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# Nondeterministic polynomial time

complexity
(NP) A set or property of computational decision problems solvable by a nondeterministic Turing Machine in a number of steps that is a polynomial function of the size of the input. The word “nondeterministic” suggests a method of generating potential solutions using some form of nondeterminism or “trial and error”. This may take exponential time as long as a potential solution can be verified in polynomial time.
NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in polynomial time) since a deterministic algorithm can be considered as a degenerate form of nondeterministic algorithm. The question then arises: is NP equal to P? I.e. can every problem in NP actually be solved in polynomial time? Everyone’s first guess is “no”, but no one has managed to prove this; and some very clever people think the answer is “yes”.
If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP.
[Examples?]
(1995-04-10)

Tagged:

• Nondeterministic turing machine

complexity A normal (deterministic) Turing Machine that has a “guessing head” – a write-only head that writes a guess at a solution on the tape first, based on some arbitrary internal algorithm. The regular Turing Machine then runs and returns “yes” or “no” to indicate whether the solution is correct. A nondeterministic Turing Machine can […]

• Non-detrimental

[de-truh-men-tl] /ˌdɛ trəˈmɛn tl/ adjective 1. causing , as loss or injury; damaging; harmful. noun 2. a detrimental person or thing. /ˌdɛtrɪˈmɛntəl/ adjective 1. when postpositive, foll by to. harmful; injurious; prejudicial: smoking can be detrimental to health adj. 1650s; see detriment + -al (1). Related: Detrimentally.

• Non-devout

[dih-vout] /dɪˈvaʊt/ adjective, devouter, devoutest. 1. devoted to divine worship or service; pious; religious: a devout Catholic. 2. expressing devotion or piety: devout prayer. 3. earnest or sincere; hearty: He had a devout allegiance to the political regime. /dɪˈvaʊt/ adjective 1. deeply religious; reverent 2. sincere; earnest; heartfelt: a devout confession adj. early 13c., from […]

• Non-diagonal

[dahy-ag-uh-nl, -ag-nl] /daɪˈæg ə nl, -ˈæg nl/ adjective 1. Mathematics. 2. having an oblique direction. 3. having oblique lines, ridges, markings, etc. noun 4. a diagonal line or plane. 5. . 6. a diagonal row, part, pattern, etc. 7. Manège. (of a horse at a trot) the foreleg and the hind leg, diagonally opposite, which […]

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