Difference between revisions 108480312 and 108480315 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|''O'']](log<sup>''c''</sup>&nbsp;''n'') using [[Big O notation|''O'']](''n''<sup>''k''</sup>) parallel processors. [[Stephen Cook]] coined the name "Nick's class" after [[Nick Pippenger]], who had done extensive research on circuits with polylogarithmic depth and polynomial size.  

Just as the class '''[[P (complexity)|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 polylogarithmic parallel computerations can be simulated by polynomial-time sequential ones. It is unknown whether '''NC''' = '''P''', but most researchers suspect this to be false, meaning that there are probably some tractable problems which are "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]]'''(contracted; show full){{DEFAULTSORT:Nc (Complexity)}}
[[Category:Complexity classes]]
[[Category:Circuit complexity]]

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