Difference between revisions 108480299 and 108480302 on dewiki

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 constants ''c'' and ''k'' such that it can be solved in time [[Big O notation|(contracted; show full)

:<math> \mathbf{NC^1 \subseteq L \subseteq NL \subseteq NC^2 \subseteq P}.</math><ref>[http://www.cs.mu.oz.au/677/notes/node18.html Nick's Class<!-- Bot generated title -->]</ref>

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.
{{fact}}

=== Open problem: Is NC proper? ===
One major open question in [[computational complexity theory|complexity theory]] is whether or not every containment in the '''NC''' hierarchy is proper. It was observed by Papadimitriou that, if '''NC'''<sup>''i''</sup> = '''NC'''<sup>''i''+1</sup> for some ''i'', then '''NC'&#x(contracted; show full){{DEFAULTSORT:Nc (Complexity)}}
[[Category:Complexity classes]]
[[Category:Circuit complexity]]

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[[es:Clase de Nick]]
[[ko:NC (복잡도)]]
[[ja:NC (計算複雑性理論)]]