Nanoscale science and computing is becoming a major research area as today's scientists try to understand the processes of natural and biomolecular computing. The field is concerned with the architectures and design of molecular self-assembly, nanostructures and molecular devices, and with understanding and exploiting the computational processes of biomolecules in nature.

This book offers a unique and authoritative perspective on current research in nanoscale science, engineering and computing. Leading researchers cover the topics of DNA self-assembly in two-dimensional arrays and three-dimensional structures, molecular motors, DNA word design, molecular electronics, gene assembly, surface layer protein assembly, and membrane computing.

The book is suitable for academic and industrial scientists and engineers working in nanoscale science, in particular researchers engaged with the idea of computing at a molecular level.

This volume is based on the workshop Modelling in Molecular Biology that tookplacein2002inSingapore. Themaingoaloftheworkshopwastopresent models/methods used in solving some fundamental problems in biosciences. The volume consists of a selection of papers presented at the workshop as well as of some other papers that are included so that the presentation of the theme of the workshop is broader and more balanced. As a matter of fact we feel that the collection of papers comprising this volume represents a wide spectrum of quite diverse ideas and trends. The paper by D. A. Beard et al. explores the common thesis that und- standingthebehaviouroflargeinteractingsystemsofmanyenzymesandre- tants underlies the modelling and simulation of whole-cell systems. Moreover, the models need to represent the basic stoichiometry, with balanced che- cal reactions and the conservation of mass, energy and charge. The authors discuss the stoichiometric and then kinetic details of approaches to modelling and simulation of biochemical systems. P. R. A. Campos et al. are concerned with models of evolution and adaptation (which is essential for precise - derstanding of molecular phylogeny). In particular, their paper is concerned with the rate of adaptation of asexual organisms(which is important because it in?uences the speed of the assumed molecular clock). It is known that for such organisms the rate of adaptation does not steadily increase with the - creasing rate of advantageous mutations, and this paper studies the mutual interference of two advantageous mutants that are each initially present in only a single organism."

This is the first text and monograph about DNA computing, a molecular approach that might revolutionize our thinking and ideas about computing. Although it is too soon to predict whether computer hardware to change from silicon to carbon and from microchips to DNA molecules, the theoretical premises have already been studied extensively. The book starts with an introduction to DNA-related matters, the basics of biochemistry and language and computation theory, and progresses to the most advanced mathematical theory developed so far in the area. All three authors are pioneers in the theory of DNA computing. Apart from being well-known scientists, they are known for their lucid writing. Many of their previous books have become classics in their field, and this book too is sure to follow their example.

This is the first monograph on computation in living cells - one of the central and fastest growing areas of research in this field. Gene assembly in ciliates (unicellular organisms) is a splendid example of such computations. This work has helped to clarify important biological aspects of gene assembly, yielded novel insights into the nature of computation, and broadened our understanding of what computation is about. The monograph gives an accessible account of both the biology and the formal analysis of the gene assembly process. It can be used as a textbook for either graduate courses or seminars.

The need for a comprehensive survey-type exposition on formal languages and related mainstream areas of computer science has been evident for some years. In the early 1970s, when the book Formal Languages by the second mentioned editor appeared, it was still quite feasible to write a comprehensive book with that title and include also topics of current research interest. This would not be possible anymore. A standard-sized book on formal languages would either have to stay on a fairly low level or else be specialized and restricted to some narrow sector of the field. The setup becomes drastically different in a collection of contributions, where the best authorities in the world join forces, each of them concentrat ing on their own areas of specialization. The present three-volume Handbook constitutes such a unique collection. In these three volumes we present the current state of the art in formallanguage theory. We were most satisfied with the enthusiastic response given to our request for contributions by specialists representing various subfields. The need for a Handbook of Formal Languages was in many answers expressed in different ways: as an easily accessible his torical reference, a general source of information, an overall course-aid, and a compact collection of material for self-study. We are convinced that the final result will satisfy such various needs."

L systems are language-theoretic models for developmental biology. They wereintroduced in 1968 by Aristid Lindenmayer (1925-1989) and have proved to be among the most beautiful examples of interdisciplinary science, where work in one area induces fruitful ideas and results in other areas. L systemsare based on relational and set-theoretic concepts, which are more suitable for the discrete and combinatorial structures of biology than mathematical models based on calculus or statistics. L systems have stimulated new work not only in the realistic simulation of developing organisms but also in the theory of automata and formal languages, formal power series, computer graphics, and combinatorics of words. This book contains research papers by almost all leading authorities and by many of the most promising young researchers in the field. The 28 contributions are organized in sections on basic L systems, computer graphics, graph grammars and map L systems, biological aspects and models, and variations and generalizations of L systems. The introductory paper by Lindenmayer and J}rgensen was written for a wide audience and is accessible to the non-specialist reader. The volume documents the state of the art in the theory of L systems and their applications. It will interest researchers and advanced students in theoretical computer science and developmental biology as well as professionals in computer graphics.

Part of the broader research field of natural computing, Membrane Computing is an area within computing science that aims to abstract computing ideas and models from the structure and functioning of living cells, as well as from the way the cells are organized in tissues or higher order structures. It studies models of computation (known as P systems) inspired by the biochemistry of cells, in particular by the role of membranes in the compartmentalization of living cells into "protected reactors."
This handbook provides both a comprehensive survey of available knowledge and established research topics, and a guide to recent developments in the field, covering the subject from theory to applications. The handbook is suitable both for introducing novices to this area of research, and as a main source of reference for active researchers. It sets out the necessary biological and formal background, with the introductory chapter serving as a gentle introduction to and overview of membrane computing. Individual chapters, written by leading researchers in membrane computing, present the state of the art of all main research trends and include extensive bibliographies.

The two-volume set originates from the Advanced Course on Petri Nets held in Dagstuhl, Germany in September 1996; beyond the lectures given there, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area.
Together with its companion volume "Lectures on Petri Nets II: Applications" this book is the actual reference for the area and addresses professionals, students, lecturers, and researchers who are
- interested in systems design and would like to learn to use Petri nets familiar with subareas of the theory or its applications and wish to view the whole area
- interested in learning about recent results presented within a unified framework
- planning to apply Petri nets in practical situations
- interested in the relationship of Petri nets to other models of concurrent systems.

This book offers an overview of the key ideas of Petri nets, how they were developed, and how they were applied in diverse applications. The chapters in the first part offer individual perspectives on the impact of Petri's work. The second part of the book contains personal memories from researchers who collaborated with him closely, in particular they recount his unique personality. The chapters in the third part offer more conventional treatments on various aspects of current Petri net research, and the fourth part examines the wide applications of Petri nets, and the relationships with other domains. The editors and authors are the leading researchers in this domain, and this book will be a valuable insight for researchers in computer science, particularly those engaged with concurrency and distributed systems.

This third volume of the Handbook of Formal Languages discusses language theory beyond linear or string models: trees, graphs, grids, pictures, computer graphics. Many chapters offer an authoritative self-contained exposition of an entire area. Special emphasis is on interconnections with logic.

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation.Over the last 25-odd years graph grammars have developed at a steady pace into a theoretically attractive and well-motivated research field. In particular, they are now based on very solid foundations, which are presented in this volume. Volume 1 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations includes a state-of-the-art presentation of the foundations of all the basic approaches to rule-based graph specification and transformation: algebraic approach, logic approach, node-based rewriting, (hyper)edge-based rewriting, programmed graph rewriting, and 2-structures. The book has been written in a tutorial/survey style to enhance its usefulness.

The theory of traces employs techniques and tackles problems from quite diverse areas which include formal language theory, combinatorics, graph theory, algebra, logic, and the theory of concurrent systems. In all these areas the theory of traces has led to interesting problems and significant results. It has made an especially big impact in formal language theory and the theory of concurrent systems. In both these disciplines it is a well-recognized and dynamic research area. Within formal language theory it yields the theory of partially commutative monoids, and provides an important connection between languages and graphs. Within the theory of concurrent systems it provides an important formal framework for the analysis and synthesis of concurrent systems.This monograph covers all important research lines of the theory of traces; each chapter is devoted to one research line and is written by leading experts. The book is organized in such a way that each chapter can be read independently - and hence it is very suitable for advanced courses or seminars on formal language theory, the theory of concurrent systems, the theory of semigroups, and combinatorics. An extensive bibliography is included. At present, there is no other book of this type on trace theory.