Polynomial time
P is the
class of languages that are decidable (solvable) in polynomial time on a
deterministic single-tape Turing machine.
P = 
TIME(nk)
There
is an important point to note about the polynomial time class of languages, P.
P
roughly corresponds to the class of problems that are realistically solvable on
a computer.
The
following table shows why.
|
|
|
Table 1: Running time
for programs of various orders
|
|
Name
|
Running Time Function
T(n)
|
Order
|
Example:
n=256 (size of input)
1 microsec/instruction
1x10-6 sec/instruction
|
|
Constant time
|
c
|
O(1)
|
|
|
Log Log
N time
|
a log log
n + b
|
O(log log n)
|
0.000003 sec
|
|
Log N time
|
a log n + b
|
O(log n)
|
0.000008 sec
|
|
Linear time
|
an + b
|
O(n)
|
0.0025 sec
|
|
N Log N time
|
a n log n + b n + c
|
O(n log n)
|
0.002 sec
|
|
Quadratic time
|
a n2 + b n + c
|
O(n2)
|
0.065 sec
|
|
Polynomial time
|
a nk
+ ...
|
O(nk)
|
17 sec (k=3)
|
|
Exponential
|
a kn
+ ...
|
O(kn)
|
3.67x1061 centuries
(k=2)
|
|