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How could we use living cells to perform computation? Would our definition of computation change as a consequence of this? Could such a cell-computer outperform digital computers? These are some of the questions that the study of Membrane Computing tries to answer and are at the base of what is treated by this monograph. Descriptional and computational complexity of models in Membrane Computing are the two lines of research on which is the focus here. In this context this book reports the results of only some of the models present in this framework. The models considered here represent a very relevant part of all the models introduced so far in the study of Membrane Computing. They are in between the most studied models in the field and they cover a broad range of features (using symbol objects or string objects, based only on communications, inspired by intra- and intercellular processes, having or not having a tree as underlying structure, etc.) that gives a grasp of the enormous flexibility of this framework. Links with biology and Petri nets are constant through this book. This book aims also to inspire research. This book gives suggestions for research of various levels of difficulty and this book clearly indicates their importance and the relevance of the possible outcomes. Readers new to this field of research will find the provided examples particularly useful in the understanding of the treated topics.

A universal goal of technological development is the enrichment of human life. The fast developments of nano/micro technologies enable us to directly handle a single cell or a single molecule. This capability propels the molecular based diagnostic and therapeutic technologies to a new horizon. In this book, we not only examine the-state- of-art biotechnologies, but also present many cutting-edge research topics which will lead toward the next generation technologies for improving human health. With the capabilities of moving, stopping, mixing and concentrating minute amount of fluid and/or particles, microfluidic circuitry provides unprecedented functions for advancing sample preparation and cell culture processes. Integrated bio-marker sensors with microfluidics, it becomes possible to detect diseases in extremely sensitive and specific manner. With the cutting edge optical techniques and proper surface molecular modification, we can study and manipulate biological processes in live cell. While we have made significant progresses in studying and controlling the phenomena in the nano/micro scale, human health is a system issue with a length in the order of a meter. A disparity of several orders of magnitude in the length scales presents significant challenges. Our current and future tasks are to develop the seamless integration processes from materials through devices and eventually into engineering systems. Our ultimate goal is that these nano/micro technology based systems can effectively interface and direct the biological complex system toward desired fate.

The vast majority of random processes in the real world have no memory — the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation procedures. Traditional books, heavy in mathematical theory, often ignore such methods and attempt to force problems into a rigid framework of closed-form solutions.