This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.

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.

Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science provides an introduction to the various aspects of theoretical computer science. Theoretical computer science is the mathematical study of models of computation. This text is composed of five parts encompassing 17 chapters, and begins with an introduction to the use of proofs in mathematics and the development of computability theory in the context of an extremely simple abstract programming language. The succeeding parts demonstrate the performance of abstract programming language using a macro expansion technique, along with presentations of the regular and context-free languages. Other parts deal with the aspects of logic that are important for computer science and the important theory of computational complexity, as well as the theory of NP-completeness. The closing part introduces the advanced recursion and polynomial-time computability theories, including the priority constructions for recursively enumerable Turing degrees. This book is intended primarily for undergraduate and graduate mathematics students.

The Mathematical Theory of L Systems

Simple EOL forms under uniform interpretation generating CF languages; Codes: unequal probabilities unequal letter costs; Sur l'inversion des morphismes d'arbres; Grammars with dynamic control sets; Ambiguite forte; Relationship between density and deterministic complexity of NP-complete languages; Stable models of typed calculi; Path measures of turing machines computations; Une famille remarquable de codes indecomposables; Comparisons and reset machines; Size-depth tradeoff in boolean formulas.

This book constitutes the refereed proceedings of the 15th International Conference on Developments in Language Theory, DLT 2011, held in Milano, Italy, in July 2011. The 34 regular papers presented were carefully reviewed and selected from numerous submissions. The volume also contains the papers or abstracts of 5 invited speakers, as well as a 2-page abstract for each of the 7 poster papers. The topics covered include grammars, acceptors and transducers for words, trees and graphs; algebraic theories of automata; codes; symbolic dynamics; algorithmic, combinatorial and algebraic properties of words and languages; decidability questions; applications of language theory, including: natural computing, image manipulation and compression, text algorithms, cryptography, concurrency, complexity theory and logic; cellular automata and multidimensional patterns; language theory aspects of quantum computing and bio-computing.