Shallow laconic P systems can count

Uniform families of shallow P systems with active membranes and charges are known to characterize the complexity class P#, since this kind of P systems are able to “count” the number of objects sent out by the dividing membranes. Such a power is absent in monodirectional systems, where no send-in rules are allowed: in this case, only languages in P∥ can be recognized. Here, we show that even a tiny amount of communication (namely, allowing only a single send-in per membrane during the computation) is sufficient to achieve the ability to count and solve all problems in the class P#∥, where all queries are performed independently.