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In [[computational complexity theory|complexity theory]], the class '''NC''' ("Nick's Class") is the set of [[decision problem|decision problems]] 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 are constants ''c'' and ''k'' such that it can be solved in time O((log ''n'')<sup>''c''</sup>) using O(''n''<sup>''k''</sup>) parallel processors.  

Just as the class [[Complexity classes P and NP|P]] can be thought of as the tractable problems, so NC can be thought of as the problems that can be efficiently solved on a parallel computer.  NC is a subset of P because parallel computers can be simulated by sequential ones. It is unknown whether NC = P, but most researchers suspect this to be false, meaning that there are some tractable problems which are probably "inherently sequential" and cannot significantly be sped up by using parallelism. Just as the class [[NP-Complete]] can be thought of as "probably intractable", so the class [[P-Complete]] can be thought of as "probably not parallelizable" or "probably inherently sequential".

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[[Stephen Cook]] coined the name NC ("Nick's class") after [[Nick Pippenger]], who had done extensive research on circuits with polylogarithmic depth and polynomial size.

==Reference==
* Greenlaw, Raymond, James Hoover, and Walter Ruzzo. ''Limits To Parallel computation; P-Completeness Theory''. ISBN 0195085914

{{ComplexityClasses}}[[Category:Complexity classes]]