(1) Any function which is the sum of constants times powers of a logarithm of the argument: f(x)=Σ_i=0^kc_ilog^p_i x. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a polylogarithmic function of the problem size, n. More formally m(n) = O(log^k n).