Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to calculate 13^8 by multiplying 13 by itself seven times, 13^8 = 13·13·13·13·13·13·13·13. However, the shortcut of squaring three times considerably speeds up the computation, 13^8 = ((13^2)^2)^2. It is often quite difficult to determine whether a given computation can be sped up by means of such a trick. Computations that cannot be sped up are said to exhibit computational irreducibility.

computational irreducibility | fast Walsh transform | principle of computational equivalence