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{{unsolved|computer science|Is '''NC''' {{=}} '''P''' ?}}
In [[computational complexity theory|complexity theory]], the class '''NC''' (for "Nick's Class") is the set of [[decision problem]]s decidable in [[polylogarithmic time]] on a [[parallel computing|parallel computer]] with a polynomial number of processors.  In other words, a problem is in '''NC''' if there exist cons(contracted; show full)

which forms the '''NC'''-hierarchy.

We can relate the '''NC''' classes to the space classes '''[[L (complexity)|L]]''' and '''[[NL (complexity)|NL]]'''.  From Papadimitriou 1994, Theorem 16.1:

:<math> \mathbf{NC}^1 \subseteq \mathbf{L} \subseteq \mathbf{NL} \subseteq \mathbf{NC}^2 \subseteq \mathbf{P}.</math>

Similarly, we have that '''NC'''
<sup>''i''</sup> is equivalent to the problems solvable on an [[alternating Turing machine]] with <math>O(\log n)</math> space and <math>(\log n)^{O(1)}</math> alternations.<ref>{{cite journal|author=S. Bellantoni and I. Oitavem|title=Separating NC along the delta axis|journal=Theoretical Computer Science|volume=318|year=2004|pages=57–78}}</ref>

=== Open problem: Is NC proper? ===
(contracted; show full)[[Category:Complexity classes]]
[[Category:Circuit complexity]]

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