NC (complexity) - Problems in NC

Problems in NC

As with P, by a slight abuse of language, one might classify function problems and search problems as being in NC. NC is known to include many problems, including

• Integer addition, multiplication and division;
• Matrix multiplication, determinant, inverse, rank;
• Polynomial GCD, by a reduction to linear algebra using Sylvester matrix (it is open whether integer GCD is in NC);
• Finding a maximal matching.

Often algorithms for those problems had to be separately invented and could not be naïvely adapted from well-known algorithms – Gaussian elimination and Euclidean algorithm rely on operations performed in sequence. One might contrast ripple carry adder with a carry-lookahead adder.