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Biological membranes play an active role in the evolution of cells over time. In the framework of Membrane Computing, P systems with active membranes capture this idea, and the possibility to increase the number of membranes during a computation. Classically, it has been considered, by using division rules, inspired in the mitosis process. Initially, the membranes in these models are supposed to have an electrical polarization (positive, negative or neutral) and the semantics is minimalist, in the sense that rules are applied in parallel, but in one transition step, each membrane can be the subject of at most one rule of types communication, dissolution or division. This paper focuses on polarizationless P systems with active membranes in which membrane creation rules are considered instead of membrane division rules as a mechanism to construct an exponential workspace, expressed both in terms of number of objects and membranes, in linear time. Moreover, the minimalist semantics is considered and some complexity results are provided in this framework, allowing to tackle the PversusNP problem from a new perspective. An original frontier of the efficiency in this context is unveiled in this paper: allowing membrane creation rules to be applicable in any membrane of the system, instead of restricting them to only elementary membranes, yields a significant boost on the computational power. More precisely, only problems in P can be efficiently solved in the restricted case, while in the non-restricted case an efficient and uniform solution to a PSPACE-complete problem is provided. [ABSTRACT FROM AUTHOR]

At the beginning of 2005, Gheorghe Păun formulated a conjecture stating that in the framework of recognizer P systems with active membranes (evolution rules, communication rules, dissolution rules and division rules for elementary membranes), polarizations cannot be avoided in order to solve computationally hard problems efficiently (assuming that P ≠ NP). At the middle of 2005, a partial positive answer was given, proving that the conjecture holds if dissolution rules are forbidden. In this paper we give a detailed and complete proof of this result modifying slightly the notion of dependency graph associated with recognizer P systems. [ABSTRACT FROM AUTHOR]

Cell division is a process that produces two or more cells from one cell by replicating the original chromosomes so that each daughter cell gets a copy of them. Membrane fission is a process by which a biological membrane is split into two new ones in such a manner that the contents of the initial membrane get distributed or separated among the new membranes. Inspired by these biological phenomena, new kinds of models were considered in the discipline of Membrane Computing , in the context of P systems with active membranes, and tissue P systems that use symport/antiport rules, respectively. This paper combines the two approaches: cell-like P systems with symport/antiport rules and membrane separation are studied, from a computational complexity perspective. Specifically, the role of the environment in the context of cell-like P systems with membrane separation is established, and additional borderlines between tractability and NP -hardness are summarized. [ABSTRACT FROM AUTHOR]

Abstract: In the literature, several designs of P systems might be found for performing the same task. The use of different techniques or even different P system models makes it very difficult to compare these designs. In this paper, we introduce a new criterion for such a comparison: the degree of parallelism of a P system. With this aim, we define the labelled dependency graph associated with a P system, and we use this new concept for proving some results concerning the maximum number of applications of rules in a single step through the computation of a P system. [Copyright &y& Elsevier]