On the power of P systems with active membranes using weak non-elementary membrane division

It is known that polarizationless P systems with active membranes can solve $$\mathrm {PSPACE}$$PSPACE -complete problems in polynomial time without using in-communication rules but using the classical (also called strong) non-elementary membrane division rules. In this paper, we show that this holds also when in-communication rules are allowed but strong non-elementary division rules are replaced with weak non-elementary division rules, a type of rule which is an extension of elementary membrane divisions to non-elementary membranes. Since it is known that without in-communication rules, these P systems can solve in polynomial time only problems in $$\mathrm {P}^{\text {NP}}$$P NP , our result proves that these rules serve as a borderline between $$\mathrm {P}^{\text {NP}}$$P NP and $$\mathrm {PSPACE}$$PSPACE concerning the computational power of these P systems.