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.

A new method to simulate restricted variants of polarizationless P systems with active membranes

According to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve $${\mathbf {NP}}$$NP-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

Minimal Parallelism and Number of Membrane Polarizations

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal.

An Improved Quantum-Inspired Evolutionary Algorithm Based on P Systems with a Dynamic Membrane Structure for Knapsack Problems

To improve the performance of Quantum-inspired Evolutionary algorithm based on P Systems (QEPS), this paper presents an improved QEPS with a Dynamic Membrane Structure (QEPS-DMS) to solve knapsack problems. QEPS-DMS combines quantum-inspired evolutionary algorithms (QIEAs) with a P system with a dynamic membrane structure. In QEPS-DMS, a QIEA is considered as a subalgorithm to put inside each elementary membrane of a one-level membrane structure, which is dynamically adjusted in the process of evolution by applying a criterion for measuring population diversity. The dynamic adjustment includes the processes of membrane dissolution and creation. Knapsack problems are applied to test the effectiveness of QEPS-DMS. Experimental results show that QEPS-DMS outperforms QEPS and three variants of QIEAs recently reported in the literature.