The counting power of P systems with antimatter

We give a characterisation of the class of problems solved in polynomial time by uniform and semi-uniform families of P systems with active membranes, using matter/antimatter annihilation rules and elementary membrane division. Like several other variants of P systems with elementary division, this class is exactly P#P, that is, the problems solvable efficiently with access to oracles for counting problems. We also consider the monodirectional case, where objects in the P system can only move from inner regions towards outer regions. In that case, the above model of P systems characterises the class P∥#P, where each query is independent of the result of the others; this contrasts with traditional P systems with active membranes, which characterise the (conjecturally proper) subclass P∥NP.