Membrane Computing after 25 Years

Natural sciences are influencing the area of information sciences, and the meaning of computation has been modified. Membrane computing is a known branch of natural computing that investigates computational techniques and models inspired by the structure and function of living cells, as well as from the organization of cells in tissues, organs, or other higher-order structures such as colonies of cells. All computational models studied in membrane computing frameworks are named P systems or membrane systems. In view of the difference of the underlying structure, P systems are classified into the following types: cell-like P systems [1,2] (a tree structure), neural-like [3], and tissue-like P systems [4] (both with an arbitrary graph structure).

The membrane computing research area was initiated in the fall of 1998 by Gheorghe Păun, and already in February 2003, the Institute for Scientific Information (ISI) considered membrane computing as an emerging research front in computer science and paper [1] as a fast-breaking paper. The membrane computing area is already well developed, both at the theoretical level and in what concerns applications, while the mention of membrane computing as a topic in the Mathematics Subjects Classification 2020 by Mathematical Reviews and zbMATH indicates its maturity. The results obtained in this field have been published in over 4000 articles, 100 PhD theses, several monographs [2,5,6,7,8,9,10,11,12,13], and a comprehensive handbook [14].

Over the years, plenty of models were presented, and their computing power was investigated. It turned out that the cell is a powerful computer as universality holds for most P systems both for symbol and string objects, working in accepting or generative ways. Universality not only holds for these classes of P systems in their most general form but also for their quite restricted forms, with restrictions on the number of membranes, form of rules, etc.

P systems can also be used to produce efficient solutions for computationally hard problems by equipping them with the ability of trading space for time in order to provide an exponential workspace generated in a reasonable amount of time. This capability has been implemented by using different mechanisms inspired by cellular mitosis (division rules), autopoiesis (creation rules), or membrane fission (separation rules), among others.

The applications to computer science are quite different as models of P systems have been employed to process a wide spectrum of problems: computer graphics, sorting/ranking, simulating and modeling circuits, cryptography, parallel architectures, and so on.

This special issue of journal Mathematics collects original research works about new advances in membrane computing:

• New membrane system architectures and variants;
• Computational power, computational complexity and computing efficiency of membrane systems;
• Applications of membrane systems for real and bio-inspired problems;
• Software tools for modeling, verification, and simulation of membrane systems.