Proof techniques in Membrane Computing

From the creation of the field of Membrane Computing in 1998, several research lines havebeen opened. On the one hand, theoretical questions like the computational power and thecomputational efficiency of P systems have been studied. In this sense, several techniquesto demonstrate the ability of these systems to provide solutions to computational problemshave been explored. The study of efficient(polynomial-time) solutions to presumably hardproblems for finding thin frontiers of efficiency is a very active area. On the other hand,several applications in biology, ecology, economy, robotics and fault diagnosis, amongothers, have been investigated. Real systems with some characteristics seem to be easyto model with membrane systems due to their behaviour. In this work, a survey of thetheoretical part will be given, explaining techniques both in the field of computabilitytheory and in the field of computational complexity theory.