Complexity theory
attempts to define such differences through a formal criterion for what is
meant by a mathematical problem feasibly be decidable , that is to say that this can be resolved by a
conventional Turing machine with a number measures which are proportional to a
polynomial function of the size of input. The category of problem with this
property is known as P ( polynomial)  and among the first three of the
abovedescribed problems. P can be shown formally distinguished from several
other classes, such as to be EXP ( exponential time).Third problem which is
fitted from above. The second problem of the above is included in a complex
class known as NP ( nondeterministic polynomial)  consists of problems that
can certainly by a computation of a nondeterministic Turing machine in a
number of steps that a polynomial function, determines the size of the input.
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The classes P and NP
P
and NP are two different complexity classes defined in two different Turing
Machine.
Pclass
is an algorithm is a member of the Ptype as required to obtain a polynomial
time to get an output, deterministically. NP –Class is an algorithm is a member
of NP. This class takes polynomial time to verify output,
nondeterministically. A Turing machine can be used synonymous with an
algorithm
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