April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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490 Design and Analysis of Algorithms
What is the relationship between various classes of problems? For example, here are a few established
relations:
LOGTIME ⊆ LOGSPACE ⊆ PTIME ⊆ PSPACE ⊆ EXPTIME ⊆ EXPSPACE . . .
We can add the prefi x N to denote non-deterministic algorithm, for example, NPTIME to denote NP.
The strictness of the following relation is not known.
PTIME ⊆ NPTIME ⊆ PSPACE
There are some dual complexity classes, like Co-NP, which a class of problems whose duals (interchange
of Yes and No answers) are in class NP. The primality problem is both in class NP and in Co-NP. It is not
known if Co-NP = NP.
On the other hand, if Co-NP ≠ NP ...
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