Tag: NC
In complexity theory, the class NC (for “Nick’s Class”) is the set of decision problems decidable in polylogarithmic time on a 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 O(log n) using O(n) 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 can be thought of as the tractable problems (Cobham’s thesis), 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 computations 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…
