Written for graduate students and advanced undergraduates in computer science, A Second Course in Formal Languages and Automata Theory treats topics in the theory of computation not usually covered in a first course. After a review of basic concepts, the book covers combinatorics on words, regular languages, context-free languages, parsing and recognition, Turing machines, and other language classes. Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method, are covered here. The author places particular emphasis on the resources needed to represent certain languages. The book also includes a diverse collection of more than 200 exercises, suggestions for term projects, and research problems that remain open.
Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences,
