Abstract biological systems as sequential machines II: Strong connectedness and reversibility

It was previously shown that the abstract biological systems called. (ℳ, ℛ)-systems could be regarded formally as sequential machines, and that when this was done, the reversibility of environmentally induced structural changes in these systems was closely related to the strong connectedness of the corresponding machines. In the present work it is shown that the sequential machines arising in this way are characterized by the property that the size of the input alphabet is very small compared with the size of the set of states of the machine. It is further shown that machines with this property almost always fail to be strongly connected. Therefore, it follows that one of the following alternatives holds: either most environmentally induced structural alterations are not environmentally reversible, or else many mappings in the category from which the (ℳ, ℛ)-systems are formed must not be physically realizable.