Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.

Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.

This book is dedicated to Aristid Lindenmayer on the occasion of his 60th birthday on November 17, 1985. Contributions range from mathematics and theoretical computer science to biology. Aristid Lindenmayer introduced language-theoretic models for developmental biology in 1968. Since then the models have been cus­ tomarily referred to as L systems. Lindenmayer''s invention turned out to be one of the most beautiful examples of interdisciplinary science: work in one area (developmental biology) induces most fruitful ideas in other areas (theory of formal languages and automata, and formal power series). As evident from the articles and references in this book, the in­ terest in L systems is continuously growing. For newcomers the first contact with L systems usually happens via the most basic class of L systems, namely, DOL systems. Here "0" stands for zero context between developing cells. It has been a major typographical problem that printers are unable to distinguish between 0 (zero) and 0 (oh). Thus, DOL was almost always printed with "oh" rather than "zero", and also pronounced that way. However, this misunderstanding turned out to be very fortunate. The wrong spelling "DOL" of "DOL" could be read in the suggestive way: DO L Indeed, hundreds of researchers have followed this suggestion. Some of them appear as contributors to this book. Of the many who could not contribute, we in particular regret the absence of A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the theory of L systems has been most significant.

This book is dedicated to Aristid Lindenmayer on the occasion of his 60th birthday on November 17, 1985. Contributions range from mathematics and theoretical computer science to biology. Aristid Lindenmayer introduced language-theoretic models for developmental biology in 1968. Since then the models have been cus­ tomarily referred to as L systems. Lindenmayer's invention turned out to be one of the most beautiful examples of interdisciplinary science: work in one area (developmental biology) induces most fruitful ideas in other areas (theory of formal languages and automata, and formal power series). As evident from the articles and references in this book, the in­ terest in L systems is continuously growing. For newcomers the first contact with L systems usually happens via the most basic class of L systems, namely, DOL systems. Here "0" stands for zero context between developing cells. It has been a major typographical problem that printers are unable to distinguish between 0 (zero) and 0 (oh). Thus, DOL was almost always printed with "oh" rather than "zero", and also pronounced that way. However, this misunderstanding turned out to be very fortunate. The wrong spelling "DOL" of "DOL" could be read in the suggestive way: DO L Indeed, hundreds of researchers have followed this suggestion. Some of them appear as contributors to this book. Of the many who could not contribute, we in particular regret the absence of A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the theory of L systems has been most significant.

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.

The book is a very up-to-date collection of articles in theoretical computer science, written by leading authorities in the field. The topics range from algorithms and complexity to algebraic specifications, and from formal languages and language-theoretic modeling to computational geometry. The material is based on columns and articles that have appeared in the EATCS Bulletin during the past two to three years. Although very recent research is discussed, the largely informal style of writing makes the book accessible to readers with little or no previous knowledge of the topics.

This proceedings volume provides a modern synopsis of recent studies concerning certain areas of language theory very close to applications. The topics covered range from image generation and developmental models to combinatorics of words and formal power series, as well as from fractals to computational complexity. Although the contributions represent ongoing research, much of the material is accessible to a reader with only a moderate previous knowledge of the subject.

The contributions of the proceedings cover almost all parts of the theory of formal languages from pure theoretical investigations to applications to programming languages. Main topics are combinatorial properties of words, sequences of words and sets of words, grammar systems and grammars with controlled derivations, generation of higher-dimensional objects and graphs, trace languages, numerical parameters of automata and languages.

The scientific developments at the end of the past millennium were dominated by the huge increase and diversity of disciplines with the common label “computer science”. The theoretical foundations of such disciplines have become known as theoretical computer science. This book highlights some key issues of theoretical computer science as they seem to us now, at the beginning of the new millennium.The text is based on columns and tutorials published in the Bulletin of the European Association for Theoretical Computer Science in the period 1995–2000. The columnists themselves selected the material they wanted for the book, and the editors had a chance to update their work. Indeed, much of the material presented here appears in a form quite different from the original. Since the presentation of most of the articles is reader-friendly and does not presuppose much knowledge of the area, the book constitutes suitable supplementary reading material for various courses in computer science.

This volume gathers lectures by 8 distinguished pioneers of automata theory, including two Turing Award winners. In each contribution, the early developments of automata theory are reminisced about and future directions are suggested. Although some of the contributions go into rather intriguing technical details, most of the book is accessible to a wide audience interested in the progress of the age of computers.The book is a must for professionals in theoretical computer science and related areas of mathematics. For students in these areas it provides an exceptionally deep view at the beginning of the new millennium.

Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.

Automata theory is the oldest among the disciplines constituting the subject matter of this Monograph Series: theoretical computer science. Indeed, automata theory and the closely related theory of formal languages form nowadays such a highly developed and diversified body of knowledge that even an exposition of "reasonably important" results is not possible within one volume. The purpose of this book is to develop the theory of automata and formal languages, starting from ideas based on linear algebra. By what was said above, it should be obvious that we do not intend to be encyclopedic. However, this book contains the basics of regular and context-free languages (including some new results), as well as a rather complete theory of pushdown automata and variations (e. g. counter automata). The wellknown AFL theory is extended to power series ("AFP theory"). Additional new results include, for instance, a grammatical characterization of the cones and the principal cones of context-free languages, as well as new decidability results.

This book is dedicated to Aristid Lindenmayer on the occasion of his 60th birthday on November 17, 1985. Contributions range from mathematics and theoretical computer science to biology. Aristid Lindenmayer introduced language-theoretic models for developmental biology in 1968. Since then the models have been cus­ tomarily referred to as L systems. Lindenmayer''s invention turned out to be one of the most beautiful examples of interdisciplinary science: work in one area (developmental biology) induces most fruitful ideas in other areas (theory of formal languages and automata, and formal power series). As evident from the articles and references in this book, the in­ terest in L systems is continuously growing. For newcomers the first contact with L systems usually happens via the most basic class of L systems, namely, DOL systems. Here "0" stands for zero context between developing cells. It has been a major typographical problem that printers are unable to distinguish between 0 (zero) and 0 (oh). Thus, DOL was almost always printed with "oh" rather than "zero", and also pronounced that way. However, this misunderstanding turned out to be very fortunate. The wrong spelling "DOL" of "DOL" could be read in the suggestive way: DO L Indeed, hundreds of researchers have followed this suggestion. Some of them appear as contributors to this book. Of the many who could not contribute, we in particular regret the absence of A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the theory of L systems has been most significant.

This book is dedicated to Aristid Lindenmayer on the occasion of his 60th birthday on November 17, 1985. Contributions range from mathematics and theoretical computer science to biology. Aristid Lindenmayer introduced language-theoretic models for developmental biology in 1968. Since then the models have been cus­ tomarily referred to as L systems. Lindenmayer's invention turned out to be one of the most beautiful examples of interdisciplinary science: work in one area (developmental biology) induces most fruitful ideas in other areas (theory of formal languages and automata, and formal power series). As evident from the articles and references in this book, the in­ terest in L systems is continuously growing. For newcomers the first contact with L systems usually happens via the most basic class of L systems, namely, DOL systems. Here "0" stands for zero context between developing cells. It has been a major typographical problem that printers are unable to distinguish between 0 (zero) and 0 (oh). Thus, DOL was almost always printed with "oh" rather than "zero", and also pronounced that way. However, this misunderstanding turned out to be very fortunate. The wrong spelling "DOL" of "DOL" could be read in the suggestive way: DO L Indeed, hundreds of researchers have followed this suggestion. Some of them appear as contributors to this book. Of the many who could not contribute, we in particular regret the absence of A. Ehrenfeucht, G. Herman and H.A. Maurer whose influence in the theory of L systems has been most significant.

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.

The book is a very up-to-date collection of articles in theoretical computer science, written by leading authorities in the field. The topics range from algorithms and complexity to algebraic specifications, and from formal languages and language-theoretic modeling to computational geometry. The material is based on columns and articles that have appeared in the EATCS Bulletin during the past two to three years. Although very recent research is discussed, the largely informal style of writing makes the book accessible to readers with little or no previous knowledge of the topics.

This proceedings volume provides a modern synopsis of recent studies concerning certain areas of language theory very close to applications. The topics covered range from image generation and developmental models to combinatorics of words and formal power series, as well as from fractals to computational complexity. Although the contributions represent ongoing research, much of the material is accessible to a reader with only a moderate previous knowledge of the subject.

The contributions of the proceedings cover almost all parts of the theory of formal languages from pure theoretical investigations to applications to programming languages. Main topics are combinatorial properties of words, sequences of words and sets of words, grammar systems and grammars with controlled derivations, generation of higher-dimensional objects and graphs, trace languages, numerical parameters of automata and languages.

The scientific developments at the end of the past millennium were dominated by the huge increase and diversity of disciplines with the common label “computer science”. The theoretical foundations of such disciplines have become known as theoretical computer science. This book highlights some key issues of theoretical computer science as they seem to us now, at the beginning of the new millennium.The text is based on columns and tutorials published in the Bulletin of the European Association for Theoretical Computer Science in the period 1995–2000. The columnists themselves selected the material they wanted for the book, and the editors had a chance to update their work. Indeed, much of the material presented here appears in a form quite different from the original. Since the presentation of most of the articles is reader-friendly and does not presuppose much knowledge of the area, the book constitutes suitable supplementary reading material for various courses in computer science.

This volume gathers lectures by 8 distinguished pioneers of automata theory, including two Turing Award winners. In each contribution, the early developments of automata theory are reminisced about and future directions are suggested. Although some of the contributions go into rather intriguing technical details, most of the book is accessible to a wide audience interested in the progress of the age of computers.The book is a must for professionals in theoretical computer science and related areas of mathematics. For students in these areas it provides an exceptionally deep view at the beginning of the new millennium.