Nested word

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Introduction to Automata Theory, Languages, and Computation

Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

Automata, Languages, and Machines

Abstract: The 80 revised papers presented together with two keynote contributions and four invited papers were carefully reviewed and sele... The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest i...

Formal Languages and Their Relation to Automata

Abstract: From the Preface (See Front Matter for full Preface) The study of formal languages constitutes an important subarea of computer science. This area sprang to life around 1956 when Noam Chomsky gave a mathematical model of a grammar in connection with his study of natural languages. Shortly afterwards, the concept of a grammar was found to be of great importance to the programmer when the syntax of the programming language ALGOL was defined by a context-free grammar. This development led naturally to syntax-directed compiling and the concept of a compiler compiler. Since then a considerable flurry of activity has taken place, the results of which have related formal languages and automata theory to such an extent that it is impossible to treat the areas separately. By now, no serious study of computer science would be complete without a knowledge of the techniques and results from language and automata theory. This book presents the theory of formal languages as a coherent theory and makes explicit its relationship to automata. The book begins with an explanation of the notion of a finite description of a language. The fundamental descriptive device--the grammar--is explained, as well as its three major subclasses--regular, context-free, and context-sensitive grammars. The context-free grammars are treated in detail, and such topics as normal forms, derivation trees, and ambiguity are covered. Four types of automata equivalent to the four types of grammars are described. These automata are the finite automaton, the pushdown automaton, the linear bounded automaton, and the Turing machine. The Turing machine is covered in detail, and unsolvability of the halting problem shown. The book concludes with certain advanced topics in language theory--closure properties, computational complexity, deterministic pushdown automata, LR(k) grammars, stack automata, and decidability.

Tree Automata Techniques and Applications

Abstract: CONTENTS 7 Acknowledgments Many people gave substantial suggestions to improve the contents of this book. These are, in alphabetic order, Introduction During the past few years, several of us have been asked many times about references on finite tree automata. On one hand, this is the witness of the liveness of this field. On the other hand, it was difficult to answer. Besides several excellent survey chapters on more specific topics, there is only one monograph devoted to tree automata by Gécseg and Steinby. Unfortunately, it is now impossible to find a copy of it and a lot of work has been done on tree automata since the publication of this book. Actually using tree automata has proved to be a powerful approach to simplify and extend previously known results, and also to find new results. For instance recent works use tree automata for application in abstract interpretation using set constraints, rewriting, automated theorem proving and program verification, databases and XML schema languages. Tree automata have been designed a long time ago in the context of circuit verification. Many famous researchers contributed to this school which was headed by A. Church in the late 50's and the early 60's: B. Trakhtenbrot, Many new ideas came out of this program. For instance the connections between automata and logic. Tree automata also appeared first in this framework, following the work of Doner, Thatcher and Wright. In the 70's many new results were established concerning tree automata, which lose a bit their connections with the applications and were studied for their own. In particular, a problem was the very high complexity of decision procedures for the monadic second order logic. Applications of tree automata to program verification revived in the 80's, after the relative failure of automated deduction in this field. It is possible to verify temporal logic formulas (which are particular Monadic Second Order Formulas) on simpler (small) programs. Automata, and in particular tree automata, also appeared as an approximation of programs on which fully automated tools can be used. New results were obtained connecting properties of programs or type systems or rewrite systems with automata. Our goal is to fill in the existing gap and to provide a textbook which presents the basics of tree automata and several variants of tree automata which have been devised for applications in the aforementioned domains. We shall discuss only finite tree automata, and the …