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.

A fundamental understanding of algorithmic bioprocesses is key to learning how information processing occurs in nature at the cell level. The field is concerned with the interactions between computer science on the one hand and biology, chemistry, and DNA-oriented nanoscience on the other. In particular, this book offers a comprehensive overview of research into algorithmic self-assembly, RNA folding, the algorithmic foundations for biochemical reactions, and the algorithmic nature of developmental processes.

The editors of the book invited 36 chapters, written by the leading researchers in this area, and their contributions include detailed tutorials on the main topics, surveys of the state of the art in research, experimental results, and discussions of specific research goals. The main subjects addressed are sequence discovery, generation, and analysis; nanoconstructions and self-assembly; membrane computing; formal models and analysis; process calculi and automata; biochemical reactions; and other topics from natural computing, including molecular evolution, regulation of gene expression, light-based computing, cellular automata, realistic modelling of biological systems, and evolutionary computing.

This subject is inherently interdisciplinary, and this book will be of value to researchers in computer science and biology who study the impact of the exciting mutual interaction between our understanding of bioprocesses and our understanding of computation.

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.

Cryptography, secret writing, is enjoying a scientific renaissance following the seminal discovery in 1977 of public-key cryptography and applications in computers and communications. This book gives a broad overview of public-key cryptography - its essence and advantages, various public-key cryptosystems, and protocols - as well as a comprehensive introduction to classical cryptography and cryptoanalysis. The second edition has been revised and enlarged especially in its treatment of cryptographic protocols. From a review of the first edition: "This is a comprehensive review ... there can be no doubt that this will be accepted as a standard text. At the same time, it is clearly and entertainingly written ... and can certainly stand alone." Alex M. Andrew, Kybernetes, March 1992

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.

Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications. So far, its usefulness has been obvious within the realm of "three C's". Computing was its original field of application, and continues to be important as regards various aspects of algorithmics and modular computations. Theory of codes and cryptography are two more recent fields of application.This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications. The book is self-contained. This means that no factual knowledge is assumed on the part of the reader. We even provide brief tutorials on relevant subjects, algebra and information theory. However, some mathematical maturity is surely a prerequisite, as our presentation is at an advanced undergraduate or beginning graduate level. We have tried to make the exposition innovative, many of the individual results being new. We will return to this matter, as well as to the interdependence of the various parts of the book, at the end of the Introduction.A special course about CRT can be based on the book. The individual chapters are largely independent and, consequently, the book can be used as supplementary material for courses in algorithmics, coding theory, cryptography or theory of computing. Of course, the book is also a reference for matters dealing with CRT.

In this book, Professor Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography. The presentation is essentially self-contained with detailed proofs of all statements provided, yet without sacrificing readability. Professor Salomaa is well known for his books in this area; the present work will be welcomed as an exposition that begins with basics familiar to advanced undergraduate students yet proceeds to some of the most important recent developments in theoretical computer science.

This book contains revised selected papers from the 18th International Conference on Membrane Computing, CMC 2017, held in Bradford, UK, in July 2017. The 18 full papers presented in this volume were carefully reviewed and selected from 29 submissions. They deal with membrane computing (P systems theory), an area of computer science aiming to abstract computing ideas and models from the structure and the functioning of living cells, as well as from the way the cells are organized in tissues or higher order structures. The volume also contains 2 invited talks.

In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography. Without sacrificing readability, the presentation is essentially self-contained, with detailed proofs of all statements provided. Professor Salomaa is well known for his books in this area. The present work provides an insight into the basics, together with explanations of some of the more important developments in the field.

This book constitutes the thoroughly refereed post-conference proceedings of the 14th International Conference on Membrane Computing, CMC 2013, held in Chi in u, Republic of Moldova, in August 2013.

The 16 revised selected papers presented together with 6 invited lectures were carefully reviewed and selected from 26 papers presented at the conference. Membrane computing is an area of computer science aiming to abstract computing ideas and models from the structure and the functioning of living cells, as well as from the way the cells are organized in tissues or higher order structures. It deals with membrane systems, also called P systems, which are distributed and parallel algebraic models processing multi sets of objects in a localized manner (evolution rules and evolving objects are encapsulated into compartments delimited by membranes), with an essential role played by the communication among compartments and with the environment."

This uniquely authoritative and comprehensive handbook is the first to cover the vast field of formal languages, as well as its traditional and most recent applications to such diverse areas as linguistics, developmental biology, computer graphics, cryptology, molecular genetics, and programming languages. No other work comes even close to the scope of this one. The editors are extremely well-known theoretical computer scientists, and each individual topic is presented by the leading authorities in the particular field. The maturity of the field makes it possible to include a historical perspective in many presentations. The work is divided into three volumes, which may be purchased as a set.

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.

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 formal language 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. The theory of formal languages constitutes the stem or backbone of the field of science now generally known as theoretical computer science.

A fundamental understanding of algorithmic bioprocesses is key to learning how information processing occurs in nature at the cell level. The field is concerned with the interactions between computer science on the one hand and biology, chemistry, and DNA-oriented nanoscience on the other. In particular, this book offers a comprehensive overview of research into algorithmic self-assembly, RNA folding, the algorithmic foundations for biochemical reactions, and the algorithmic nature of developmental processes.

The editors of the book invited 36 chapters, written by the leading researchers in this area, and their contributions include detailed tutorials on the main topics, surveys of the state of the art in research, experimental results, and discussions of specific research goals. The main subjects addressed are sequence discovery, generation, and analysis; nanoconstructions and self-assembly; membrane computing; formal models and analysis; process calculi and automata; biochemical reactions; and other topics from natural computing, including molecular evolution, regulation of gene expression, light-based computing, cellular automata, realistic modelling of biological systems, and evolutionary computing.

This subject is inherently interdisciplinary, and this book will be of value to researchers in computer science and biology who study the impact of the exciting mutual interaction between our understanding of bioprocesses and our understanding of computation.

This book constitutes the thoroughly refereed post-conference proceedings of the 12th International Conference on Membrane Computing, CMC 2011, held in Fontainebleau, France, in August 2011. The 19 revised selected papers presented were carefully reviewed and selected from 27 papers and 5 posters presented at the conference. The book also contains full papers or extended abstracts of the 5 invited presentations. The papers address all the main directions of research in membrane computing, ranging from theoretical topics in the mathematics and computer science to application issues.

J.UCS is the electronic journal that covers all areas of computer science. The high quality of all accepted papers is ensured by a strict review process and an international editorial board of distinguished computer scientists. The online journal J.UCS is a prototype for modern electronic publishing. Distributed via the Internet, it supports all the search and navigation tools of advanced online systems. This first annual print and CD-ROM archive edition contains all articles published online in J.UCS during 1995. It allows easy and durable access without logging onto the Internet. Uniform citation of papers is guaranteed by identical page numbering and layout of all versions.
J.UCS is based on HyperWave (formerly Hyper-G), a networked hypermedia information system compatible with other systems.

This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.

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."

Cryptography, secret writing, is enjoying a scientific renaissance following the seminal discovery in 1977 of public-key cryptography and applications in computers and communications. This book gives a broad overview of public-key cryptography - its essence and advantages, various public-key cryptosystems, and protocols - as well as a comprehensive introduction to classical cryptography and cryptoanalysis. The second edition has been revised and enlarged especially in its treatment of cryptographic protocols. From a review of the first edition: "This is a comprehensive review ... there can be no doubt that this will be accepted as a standard text. At the same time, it is clearly and entertainingly written ... and can certainly stand alone." "Alex M. Andrew, Kybernetes, March 1992"

This is the first book on DNA computing, a molecular approach that may revolutionize computing-replacing silicon with carbon and microchips with DNA molecules. The book starts with an introduction to DNA computing, exploring the power of complementarity, the basics of biochemistry, and language and computation theory. It then brings the reader to the most advanced theories develop thus far in this emerging research area.

This volume contains a selection of papers presented at the 10th Workshop on Membrane Computing, WMC 2009, which took place in Curtea de Arge, s, Romania, during August 24-27, 2009. The?rstthreeWorkshopsonMembraneComputingwereorganizedinCurtea de Arge, s, Romania - they took place in August 2000 (with the proceedings p- lished in Lecture Notes in Computer Science, volume 2235), in August 2001 (with a selection of papers published as a special issue ofFundamenta Inform- icae, volume 49, numbers 1-3, 2002), and in August 2002 (with the proceedings publishedinLectureNotesinComputerScience, volume2597).Thenextsixwo- shopswereorganizedinTarragona, Spain(inJuly2003), inMilan, Italy(inJune 2004), in Vienna, Austria (in July 2005), in Leiden, The Netherlands (in July 2006), in Thessaloniki, Greece (in June 2007), and in Edinburgh, UK (in July 2008), with the proceedings published as volumes 2933, 3365, 3850, 4361, 4860, and5391, respectively, ofSpringer'sLectureNotesinComputerScience. The workshop changed its name in 2010, and the series will continue as the Conference on Membrane Computing, with the next edition, CMC11, to be held in Jena, Germany. The tenth edition of WMC took place in Hotel Posada in Curtea de Arge, s (http: //www.posada.ro/)anditwasorganizedbytheNationalCollege"Vlaicu Voda" ? of Curtea de Arge, s, the University of Pite, sti, Romania, and the Institute of Mathematics of the Romanian Academy, Bucharest, under the auspices of the European Molecular Computing Consortium (EMCC) and IEEE Compu- tional Intelligence Society EmergentTechnologies Technical Committee Mole- lar Computing Task Force, with the ?nancial and organizational support of the Council of Arge, s County and Seville University."

This volume contains a selection of papers presented at the 9th Workshop on Membrane Computing, WMC9, which took place in Edinburgh, UK, during July 28-31,2008. The ?rst three workshopson membrane computing were or- nized in Curtea de Arge, s, Romania - they took place in August 2000 (with the proceedings published in Lecture Notes in Computer Science, volume 2235), in August 2001 (with a selection of papers published as a special issue of Fun- menta Informaticae, volume 49, numbers 1-3, 2002), and in August 2002 (with the proceedings published in Lecture Notes in Computer Science, volume 2597). The next ?ve workshops were organized in Tarragona, Spain, in July 2003, in Milan, Italy, in June 2004, in Vienna, Austria, in July 2005, in Leiden, The Netherlands, in July 2006, and in Thessaloniki, Greece, in June 2007, with the proceedings published as volumes 2933, 3365, 3850, 4361, and 4860 of Lecture Notes in Computer Science."

This book constitutes the thoroughly refereed extended postproceedings of the 8th International Workshop on Membrane Computing, WMC 2007, held in Thessaloniki, Greece, in June 2007 under the auspices of the European Molecular Computing Consortium (EMCC).

The 22 revised full papers presented together with 5 invited papers went through two rounds of reviewing and improvement. The papers in this volume cover all the main directions of research in membrane computing, ranging from theoretical topics in mathematics and computer science to application issues. A special attention was paid to the interaction of membrane computing with biology and computer science, focusing both on the biological roots of membrane computing, on applications of membrane computing in biology and medicine, and on possible electronically based implementations.

The present volume is based on papers presented at the 6th Workshop on M- brane Computing, WMC6, which took place in Vienna, Austria, in the period July 18-21, 2005. The ?rst three workshops were organized in Curtea de Arge, s, Romania - they took place in August 2000 (with the proceedings published in Lecture Notes in Computer Science, volume 2235), in August 2001 (with a sel- tion of papers published as a special issue of Fundamenta Informaticae, volume 49, numbers 1-3, 2002), and in August 2002 (with the proceedings published in Lecture Notes in Computer Science, volume 2597). The fourth and the ?fth workshopswereorganizedinTarragona, Spain, in July2003, andin Milan, Italy, in June 2004, with the proceedings published as volumes 2933 and 3365, resp- tively, of Lecture Notes in Computer Science. The pre-proceedingsof WMC6 were published by the Institute for Computer Languages of the Vienna University of Technology, and they were available d- ing the workshop. Conforming with tradition, this workshop, too, was a lively scienti?c event, with many questions and engaged discussions following pres- tations of papers. Thecurrentvolumeisbasedonaselectionofpapersfromthepre-proceedings. These papers were signi?cantly modi?ed according to the discussions that took placeduringtheworkshop, andalltheselectedpaperswereadditionallyrefe