Feedback in Homomorphic Realizations

It is known that for every integer d there are transition functions not isomorphically realizable by any net having feedback indegree (the largest number of wires that any delay receives from other delays in its feedback loop) less than d. Here we show that, in contrast to the isomorphic case, every transition function can be homomorphically realized by nets of feedback indegree not exceeding 2. This is a least upper bound, since simple nets (i. e., those having feedback indegrees not exceeding 1) are shown not to be universal in this sense.