The prefix problem consists of computing all the products $x_{0}x_{1} \ldots x_{j} (j = 0, \ldots,N - 1)$, given a sequence $x =(x_{0},x_{1},\ldots, x_{N-1})$ of elements in a semigroup. It is shown that there are unbounded fan-in and fan-out boolean circuits for the prefix problem with constant depth and linear size if and only if the Cayley graph of the semigroup does not contain a special type of cycle called monoidal cycle.