In paper [1] we presented, using mutual mobile membranes, a semi-uniform polynomial solution for a weak NP-complete problem (the partitioning problem). A P system computes the evolution from an initial configuration, applying rules in a maximal parallel manner, and stopping when no more rule can be applied. The final configuration is considered to be the result of the performed computation. Mobile membrane systems represent a variant of P systems with active membranes in which the evolution of membranes is given by operations inspired by biology, called endocytosis and exocytosis. Interactions in such a system take place mainly in the hierarchical structure of membranes. In the case of mutual mobile membranes these operations occur when there is cooperation between the membranes, represented by the existence of objects together with their complements within these membranes. For certain classes of mobile membrane results already exist in the literature regarding their complexity (see for example [PaAl06]). Paper [1] helps strengthen the complexity theory where mobility is used in the context of membrane systems. The main result of the paper is the demonstration that the problem of partitioning a set into two subsets with equal sums can be solved using a semi-uniform family of mutual mobile membrane systems in linear time relative to input size. In the technical report [4] we made an extension of the work [1], i.e. we presented a semi-uniform polynomial solution for a variety of NP-complete problems using mutual mobile membranes. Besides the partitioning problem, we introduced in [4] polynomial solutions also for the knapsack problem and the subset sum problem (details on these problems can be consulted in [GaJo79]). For each built solution we stated correspondence between the instantiation of the considered problem  and defining parameters representing membrane systems solutions.

In paper [2] we studied the computing power of enhanced mobile membrane systems. This class of membrane systems has been proposed for describing some biological mechanisms of the immune system. The mobility operations used are: endocytosis, exocytosis, forced endocytosis and forced exocytosis. Universality is obtained using system of 12 membranes, while systems with 8 membranes are able to describe PsET0L, while those with 3 membranes can be described by PsMAT.

In book [3] we analyzed and compared the formal descriptions of mobility in process algebras and formalisms inspired by biology. This monograph shows the results previously obtained and is the starting point for the documentation made during this period. Robin Milner introduced a first formalism is which the central idea is that of ​​mobility, pi-calculus [Milner99]. This process algebra is a model for concurrent systems adapted from process calculi with communicaton. Other process calculi considered after the appearance of pi-calculus are different variants (with ingredients such as time or location specific life processes) and mobile ambients [CaGo00] or brane calculi [Card04]. The latter is intended to abstract and is inspired by the biological processes of endocytosis, exocytosis and mitosis. Mobility is present, often as the main ingredient, in other formalisms inspired by biology that do not have an algebraic representation. Among these we mainly studied membrane systems, following the links to other such formalisms like Petri nets. We highlighted how mobility in process calculi is correlated with the processes in membrane systems, presenting a number of constructions through which an algebraic formalism can be seen as a P system and the other way around. These constructins represent a starting point for getting results relative to the project objectives planned for 2012 (complexity, computability and causality in membrane systems).