Ladner's theorem

Ladner's theorem

In computational complexity, Ladner's theorem asserts that, if the computational classes P and NP are not equal, the latter contains problems that are neither in P nor NP-complete.

Problems that are in NP but are neither in P nor NP-complete are sometimes called NP-intermediate. Ladner's theorem exhibits a problem that is NP-intermediate provided that P is not equal to NP. The problem it exhibits is defined ad-hoc for the proof and is otherwise uninteresting. It is an open question whether any "natural" problem has the same property;some problems that are considered good candidates for being NP-intermediate if P is not equal to NP are the graph isomorphism problem, factoring, and computing the discrete logarithm.

References

*cite journal
first=Richard
last=Ladner
title=On the Structure of Polynomial Time Reducibility
journal=Journal of the ACM (JACM)
volume=22
issue=1
year=1975
pages=155–171
doi=10.1145/321864.321877

* [http://users.comlab.ox.ac.uk/luke.ong/teaching/complexity/section5.ps Basic structure, Turing reducibility and NP-hardness]
* [http://weblog.fortnow.com/media/ladner.pdf Two Proofs of Ladner’s Theorem]
* [http://www.cs.umd.edu/~jkatz/complexity/lecture2.pdf NP completeness]


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