The Class NP
NP is the class of all problems that can be solved in polynomial time on a nondeterministic computer.
A nondeterministic computer always makes the correct choice at a choice point (one choice but never backs up).
Alternatively: a nondeterministic computer makes k copies of itself to run in parallel at a k-wise choice point, for all values of k.
Alternatively: a nondeterministic computer can explore a tree of depth d in O(d) time.