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What (who) is nondeterministic polynomial-time - definition
Nondeterministic time; Non-deterministic time
nondeterministic polynomial time
COMPUTATIONAL COMPLEXITY CLASS OF DECISION PROBLEMS SOLVABLE BY A NON-DETERMINISTIC TURING MACHINE IN POLYNOMIAL TIME
NP (complexity class); Nondeterministic polynomial time; NP-problem; NP-Problem; NP class; NP Class; NP-Class; NP-class; Class NP; Complexity class NP; Nondeterministic Polynomial; Nondeterministic polynomial; Np (complexity); NP (class)
<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.
See also Co-NP, NP-complete.
[Examples? ]
(1995-04-10)
Polynomial hierarchy
![PH]], and [[PSPACE]]](https://commons.wikimedia.org/wiki/Special:FilePath/Complexity-classes-polynomial.svg?width=200 "PH]], and [[PSPACE]]")
HIERARCHY OF COMPLEXITY CLASSES BETWEEN P AND PSPACE
Polynomial time hierarchy; Polynomial-time hierarchy; NP^NP; Sigma2p
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP.Arora and Barak, 2009, pp.
HOMFLY polynomial
TWO-VARIABLE KNOT POLYNOMIAL, GENERALIZING THE JONES AND ALEXANDER POLYNOMIALS
HOMFLY(PT) polynomial; HOMFLY; LYMPHTOFU polynomial; HOMFLYPT polynomial; Homfly polynomial; FLYPMOTH polynomial; HOMFLY invariant
In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e.
Wikipedia
NTIME
In computational complexity theory, the complexity class NTIME(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time O(f(n)). Here O is the big O notation, f is some function, and n is the size of the input (for which the problem is to be decided).
