Difference between revisions 108480218 and 108480225 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 <math>c</math> and <math>k</math> such that it can be solved in time <math>O((\log n)^(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 L \subseteq NL \subseteq NC^2
 \subseteq 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.

=== Open problem: Is '''NC''' proper? ===

(contracted; show full){{ComplexityClasses}}

[[Category:Complexity classes]] [[Category:Circuit complexity]]

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