Time-bounded computations - The time complexity classes P and EXP
3 important questions on Time-bounded computations - The time complexity classes P and EXP
The complexity class P
P = U k>=1 DTIME(n^k) = DTIME(n) u DTIME(n^2) etc...
normal words : contains all decidable problems that can be solved in polynomial running time
The complexity class EXP
EXP = Uk>=1 DTIME(2^n^k) = DTIME(2^n) U DTIME(2^n^2) etc....
normal words : contains all decidable problem that can be solved in exponential running time .
P included in EXP
Time Hierarchy theorem
Let f : N -> R+ be a time-honest function. Then, there exists a language A that can be decided in running time O(f(n)), but not in running time O(f(n).log_2(n))
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