Descriptive Complexity

book is dedicated to Daniel and Ellie. Preface This book should be of interest to anyone who would like to understand computa-tion from the point of view of logic. The book is designed for graduate students or advanced undergraduates in computer science or mathematics and is suitable as a textbook or for self study in the area of descriptive complexity. It is of particular interest to students of computational complexity, database theory, and computer aided verification. Numerous examples and exercises are included in the text, as well as a section at the end of each chapter with references and suggestions for further reading. The book provides plenty of material for a one semester course. The core of the book is contained in Chapters 1 through 7, although even here some sections can be omitted according to the taste and interests of the instructor. The remain-ing chapters are more independent of each other. I would strongly recommend including at least parts of Chapters 9, 10, and 12. Chapters 8 and 13 on lower bounds include some of the nicest combinatorial arguments. Chapter 11 includes a wealth of information on uniformity; to me, the low-level nature of translations between problems that suffice to maintain completeness is amazing and provides powerful descriptive tools for understanding complexity. I assume that most read-ers will want to study the applications of descriptive complexity that are introduced in Chapter 14